Focusing on Presbyopia Correction with Simulation

Presbyopia is an eye disorder that results in the loss of the near vision. The World Health Organization (WHO) says that “uncorrected presbyopia is the most common cause of visual impairment” — and it becomes more prevalent as we get older, with an onset at around 45 years old.

While we’re young, visual accommodation helps our eyesight to naturally adapt its distance of focus for far and near objects. Among other factors, the crystalline lens of the eye is able to change its shape through a complex biomechanical process that causes far vision to be passive and near vision to be active. However, as we age, geometric changes happen in the lens. The growth of the lens and the mechanical property change of the lens (the lens gets stiffer) cause the ciliary ring to be pushed forward. Lens compliance is affected more and more until the amplitude of deformation is almost nonexistent between far and near vision. The lens’ shape increases, and its equivalent refractive power and overall diameter decrease to the point that, in cases of presbyopia, the most accommodated shape ends up being the far vision.

Anatomy of a human eye for the near and far vision, with the main structures involved in the accommodation process labeled. Image courtesy Kejako.

While corrective lenses, such as eyeglasses, are the safest and most reliable way to address vision problems associated with presbyopia, they do not address every problem associated with the presbyopia — and not everyone likes wearing spectacles.

Reading glasses have been around for quite a while to help correct visual impairment from disorders like presbyopia. This painting, called the “Glasses Apostle”, was painted by Conrad von Soest in 1403. Image in the public domain in the United States, via Wikimedia Commons.

Some people choose to undergo refractive surgery to address this type of near-vision loss. Currently, this surgery is invasive and can still come with visual compromises — patients may experience vision that produces a glare or halo or have problems seeing in dim lighting. Further, many in vivo imaging technologies available for these procedures are not able to accurately account for every factor or practical clinical measurement in the visual accommodation process.

Left: Halos at night. Right: Glare at night. Images courtesy Kejako.

To address these limitations as well as the root problem of presbyopia, David Enfrun, Aurélien Maurer, and Charles-Olivier Zuber at Kejako developed a 3D parametric mechanical model of the human eye as well as an optical evaluation technique using the COMSOL® software. According to Enfrun, cofounder and CEO of Kejako, the research team "decided to approach ophthalmology with an antiaging mindset," so they turned to simulation in order to look for a "biomechanical alternative to reading glasses and heavy surgeries." With their model, the team can use a reverse engineering technique to deduce nonmeasurable properties from in vivo imaging.

Modeling Solutions to the Age-Old Problem of Presbyopia

Because the visual accommodation process is so complex, simplifications are often made when it comes to modeling the eye and its components. For instance, many models are axisymmetric and do not account for the natural variability of the organs of the eye. The models focus on either the accommodation’s mechanical or optical aspects, meaning only a few of the eye components are modeled and material properties are approximated rather than taking real behaviors into account.

In vivo technologies for ophthalmology have contributed greatly to advances in 3D modeling, but each type has its pros and cons:

• Magnetic resonance imaging (MRI) provides the best results (low distortion, high resolution) for internal geometry but is hard to use outside of labs
• Optical coherence tomography (OCT) helps retrieve info on the optical axis but induces some spatial distortions
• Ultrasound biomicroscopy (UBM) gets images of nontransparent eye parts but induces high spatial distortions

After making corrections and extrapolating information from in vivo imaging, some material properties are still difficult to measure. What’s more, nonmeasurable properties are often essential when trying to correct presbyopia, such as the stiffness and the refractive index distribution in the crystalline lens.

Setting Up an Optomechanical Model of the Human Eye

In an effort to obtain this important data, the Kejako research team built a model of their own using the Nonlinear Structural Materials Module, Structural Mechanics Module, and Ray Optics Module; add-on products to the COMSOL Multiphysics® software.

First, they developed and validated a complete 3D nonaxisymmetric model of the human eye’s accommodation that includes the main organs involved in the visual accommodation process. Since the validated model proved capable of simulating presbyopia progression, the researchers were able to further develop the model geometries, including accounting for both nearsighted and farsighted geometries.

The parametric optomechanical model of the human eye developed by Kejako. Image courtesy Kejako.

The research team also used the CAD Import Module to prepare the model geometries based on an OCT scan of a relatively young eye belonging to a 22-year-old patient. While they used this imaging as a basis for their model, the researchers will eventually be able to help customize patient procedures by importing each patient’s biometry data into the model so they can “have an exact representation of each patient’s eye and its actual presbyopia stage.”

This could significantly advance presbyopia treatment, as according to Maurer, the current implant market is “like a ready-to-wear shop for shoes: a bunch of different sizes.” However, each person’s eye is different; the distances between components and their individual shapes creating a unique combination. In addition, Zuber says that not all patients at a given age are experiencing the same stage of presbyopia when it comes to lens hardening, and the lens properties are not “evenly distributed among patients.” Using simulation could help create optimized laser treatments that fit each person’s needs. As Maurer explains, “the combination of imaging, simulation, and laser enables us to make a patient-specific treatment.”

The OCT imaging provided the team with geometries in the optical axis for two optical stimuli: 0D for far vision and 6D for near vision. Measured in diopters, these geometries indicate the power of the lens and its ability to focus light on the retina. They used additional measurements and properties from validated experiments and reference data. The researchers were then able to submit the sample tissue to both mechanical and optical tests to increase their ability to obtain more material properties. The model was considered ready once the unaccommodated geometry entered a tolerance of +/-5% with the far vision measurement. (For more details, take a look at Kejako’s research paper, which was presented at the COMSOL Conference 2017 Rotterdam.)

OCT imaging of the subject (left) alongside a CAD simulation (right). Images courtesy Kejako.

Deducing the Refractive Index for 2 States of Vision

To model the refraction of the lens, the researchers used the Wall Distance interface to create a repartition of the refractive index that follows the deformation of the lens during accommodation. The team’s goal was to compute the refractive index and its spatial distribution for both farsighted vision and nearsighted vision conditions.

In their first study (“Test A”), they prepared the geometry to account for these extreme conditions, hypothesizing that the refractive index is homogeneous in the lens. They then applied a two-parameter function to the generated distance field to create a gradient of refractive index (GRIN) that lined up with natural optical properties.

Left: A GRIN measured with MRI. Image from S. Kasthuriranagan et al., “In Vivo Study of Changes in Refractive Index Distribution in the Human Crystalline Lens with Age and Accommodation“, 2018. Right: Simulation showing 3D cuts of the distance gradient generated with the Wall Distance interface. Image courtesy Kejako.

The second study they prepared (“Test B”) focused on the model of the GRIN. By running parametric sweeps, the researchers sought to extract a unique couple of parameters for the GRIN that match both vision states.

Map of a GRIN that matches the two states of vision. Image courtesy Kejako.

Evaluating the Simulation Results

After examining the overall simulation, the researchers were able to verify that their results for the 3D parametric human eye model geometry were consistent with scientific literature. For instance, the far-vision data has a less than 3% difference in the lens position and shape. In addition, the researchers found that the results for the individual studies are consistent with validated data. The values they obtained in Test A are well within the range of the equivalent measurements from verified studies, and the GRIN results in Test B are consistent for both visual conditions.

Based on these two studies, the team found some surprising results that helped inform their research and reverse engineering capabilities. For instance, contrary to their hypothesis that the refractive index is homogeneous in the lens, the results for Test A show that a unique homogeneous refractive index matching the amplitude of the patient’s stimuli (0 to 6D) could not be found. In addition, when the far-vision-matching homogeneous refractive index is used for near vision, it induces an accommodation amplitude of 4.35D instead of 6D — the homogeneous refractive index value needs to be much higher when computed for near vision.

Based on their GRIN model results, the researchers also found something interesting concerning the natural optical structure: The human eye will induce a nonlinear response to try to maximize the optical power of the lens tissue. As shown below, to achieve the same maximal value of the plateau, the gradient induces bigger changes than the maximal values.

Effect of two different GRIN intensity parameters with the same plateau value in the far vision. Image courtesy Kejako.

Furthermore, due to the natural optical structure, the eye has a greater range of focus with a lower maximal value of the refractive index. Shown below is a schematic of the GRIN acting as a multiplicative factor for the accommodation. For each state of vision, the lens tissues move with the accommodation. The optical configuration for far vision is clearly quite different than the configuration for near vision. By inducing this nonlinear response, the GRIN contributes to improving the amplitude of vision.

Finite multilayer representation of the GRIN with decomposition in equivalent lenses for each layer. Image courtesy Kejako.

Deducing nonmeasurable properties like the ones above could lead to important developments in eye care, such as the prevention and correction of presbyopia. The Kejako researchers quickly understood the value of this ability in the ophthalmology field. After developing and validating their model, they opened an internal department dedicated to answering research and development questions that their tools and simulations can help answer.

The Future of Simulation in Eye Care

In the future, simulation could help the team learn more information, such as what effect laser treatment has on a patient’s amplitude of accommodation. The reverse engineering technique could also come into play in their plans to determine the mechanical properties of a lens from elastography imaging.

Already, their model results have helped answer some questions about visual accommodation. Soon, the researchers hope their model will not be limited to visual accommodation and can be used in diagnostics and the optimization of personalized medical procedures as well. To accomplish this, the team is working on improving the eye model so that they can simulate potential solutions for treating presbyopia.

Enfrun explains that they’re further developing the model for lab testing by “increasing the physical interpretation of what can happen in lab testing,” whether ex or in vivo (currently, the researchers are testing ex vivo feasibility). With improvements like this, the model could reduce the number of biological (e.g., in vivo) tests needed, which was one of the team’s goals. Enfrun says they chose simulation “as a tool for us to understand the visual accommodation process without further ex vivo/in vivo testings.”

For more information about the 3D full-eye model, you can read the research paper by clicking the button below:

Learn even more about Kejako’s optomechanical modeling research on pages 6–9 of Multiphysics Simulation 2018.

The Example: Laser Heating of a Flat Plate

Let’s consider the case of a flat plate of material that is being heated by a laser heat source. The plate is centered at the origin, as shown in the figure below, and we want to heat its surface at varying locations over time. Suppose that the laser (or the workpiece) is mounted on a stage that provides positional control of the focus point. Let’s also assume that there are some optics that shape the beam profile of the laser, so the heat source is spread over a small area around the focus.

Schematic of a laser heat source traversing over a workpiece.

Now, let’s look at several different ways in which we can define the moving focus point to follow a known tool path.

Method 1: Using Variables

The simplest approach is to use a set of variables to define the position of the focus and distribution of the heat load over time. Let’s say that we want to have a 1-kW total heat load moving in a 40-cm radius circular path every 10 s. Furthermore, the heat load has a Gaussian intensity distribution with a 5-cm waist radius. We can define this information using variables, as shown in the screenshot below.

The first four definitions, Rb, P0, Rp, and T0, are actually just constants. If we would like to alter any of these definitions via a parametric sweep later on, we could also define them as Global Parameters. For now, it is simplest to just show them all in one place.

The next two variables, x_focus and y_focus, are not constant: They vary as a function of time, the built-in variable t. We can see that these variables describe a point moving on a circular path about the origin as:

Rp*cos(2*pi*t/T0)

Rp*sin(2*pi*t/T0)

The next variable, R, is a function of time and space. It makes use of the coordinate variables x and y, as well as x_focus and y_focus, which we just saw are functions of time. So at each instant in time and at every point in space, this variable tells us the distance (in the xy-plane) from the laser focal point.

The last variable, HeatFlux, is a function of R and the constants. It defines a Gaussian intensity profile about the focal point such that the total heat flux equals the defined power. It is this variable, HeatFlux, that we enter as a boundary condition, as shown in the screenshot below.

This prescribed heat flux expression then gives the heating profile path visualized below.

A circular heating profile set up via the Variables node.

Method 2: Using Interpolation Functions

So far, this isn’t very complicated; just a few expressions. But we can replace the simple expressions for x_focus and y_focus with something more general. COMSOL Multiphysics provides a variety of built-in functions in the software. For our discussion here, the most useful is the Interpolation function, which lets us read in data from a text file. Let’s suppose we have a text file containing rows of data of time and the x- and y-locations of the laser focus at that time. A sample of such a file is shown below:

Such data can be read in to the Interpolation function using the settings shown below. Note that there is just a single argument here, time, and the two columns of data after that represent the x-focus and y-focus, respectively, in units of centimeters. Between the specified points in time, we want the laser to move linearly. We specify the function names as x_f and y_f, respectively, and make sure to set the arguments correctly.

We can then just alter our previous expressions for the focus to be x_focus = x_f(t) and y_focus = y_f(t) and get the moving load pictured below.

A heating profile read in from a text file.

We can see that this Interpolation function quickly lets us read in some very complicated profile patterns, we just need a way to generate these profiles and the text files. For example, the text file format used here is not too different from the G-code format, so if you have a heating path defined in such a format, it can be pretty simple to convert it to a COMSOL®-friendly input. On the other hand, maybe we would like to import a profile created in the ubiquitous 2D DXF file format. Let’s look at that next…

Method 3: Using Paths Imported from CAD Geometries

Suppose we want the load to move along a path we read in from an external file, as shown in the image below. We would like the laser to move smoothly along this path from one end to the other. Now, we need to do a bit more work.

The S-shaped profile of the laser path is read in from a DXF file as a geometry.

The file that we’ve read in doesn’t have any information about time within it: It is just a path that we expect the laser to follow at a constant speed. Now, each edge of this imported path (and there may be thousands of edges) does have parameters s1 and s2 that vary linearly along the length, but if there are many edges, we probably wouldn’t want to work with these parameters. So instead, how do we compute where the laser is at every point in time along the entire set of lines? One way in which we can do this is by introducing another partial differential equation (PDE) to solve, along the desired set of lines. The PDE we want to solve is:

where refers to the tangential direction to the curve.

This PDE, along with the boundary conditions of u = 0 at one end of the path and u = 1 at the other end, will give us a field along the path that varies linearly from 0 to 1, which will be proportional to the total arc length of all of the edges. We can set this up using the Coefficient Form Edge PDE interface, as shown in the screenshots below. All coefficient terms other than the Diffusion Coefficient, c, are set to zero.

Left: Settings of the Coefficient Form Edge PDE interface needed to compute the path. Right: The diffusion coefficient term, c, is a constant; all other coefficients are set to zero.

Then, two Dirichlet boundary conditions set the field, u, at either ends, and we solve this PDE in a stationary step, prior to solving the heat transfer problem but still within the same study.

Two Dirichlet boundary conditions are used at the start and end of the profile path to constrain the field.

Next, we introduce a single minimum component coupling operator into the model, with the source selected as the edges to follow. This minimum operator is used to define the focal point coordinates, e.g.:

x_focus = minop1(abs(u-t/T0),x)

y_focus = minop1(abs(u-t/T0),y)

Note that the minimum operator is given two arguments. When we call the operator with two arguments, it will return the value of the second argument where the first argument is at a minimum. Thus, at each time, t, it will return the x- and y-locations of a point on the edge that is t/T0 fraction of the way from one end to the other.

Left: The minimum operator is defined over the path that the heat source follows. Right: The laser heat source following the path defined by an imported DXF file.

And what if we would like the laser to traverse different parts of the path at different speeds? We would just need to adjust the coefficient, c, along those sets of edges. Suppose we want the laser to move three times faster along the curved boundaries than along the straight lines: just make c three times larger. Note that the absolute value doesn’t matter, it is just the ratio of the coefficient magnitudes that matters. The one drawback to this approach arises when the path crosses itself. In that situation, you would need to subdivide the path into two, or more, groups of paths; solve a PDE on each; and do a bit more bookkeeping for the variables.

Closing Remarks on Modeling Moving Loads and Constraints

In this blog post, we have looked at three different approaches of modeling a moving load. To try them yourself, click the button below to head to the Application Gallery. There, you can download the MPH-files for the models featured above (must have a COMSOL Access account and valid software license).

Several other examples within the Application Gallery also make use of these techniques, including:

• Laser Heating of a Silicon Wafer
• Traveling Load

Although in this blog post we only considered loads, note that we can also apply these techniques to constraints, as described in How to Make Boundary Conditions Conditional in Your Simulation.

Do you have further questions about using COMSOL Multiphysics for your modeling applications? Please let us know!

Can we “see” sound? Not directly, but we can come close. By changing our perspective, we can learn a lot about the nature of acoustics. One way to observe acoustics phenomena is by studying standing waves in a solid medium known as a Chladni plate. A special technique creates patterns on the plate that reveal sound’s physical nature.

Visualizing the Resonance of Musical Instruments

Imagine you’re at a classical music concert. The orchestra has finished warming up. The lights dim. A single spotlight appears on the violin soloist as she moves front and center stage. She raises her bow and a hush falls over the audience as you anticipate her first, resounding note. The violinist draws the bow across the string…and the note that results carries beautifully, reverberating throughout the auditorium for your listening pleasure.

Musicians warming up on stage before performing. Image by Jiaqian AirplaneFan — Own work. Licensed under CC-BY 3.0, via Wikimedia Commons.

Aside from the violinist’s talent and training, the quality of the violin plays a large role in the sound produced. Musicians are very particular about their instruments, and rightly so, because an instrument’s design affects its resonance. For instance, when bowing a string, the string vibrates at a certain frequency, which is measured by how many times per second it oscillates back and forth. It’s critical that the bridge and body of a violin are optimized to transmit the energy of that vibration — otherwise, the resonance will be minimal.

Violins and other string instruments are designed and constructed by testing the optimal position of the holes, thickness of the wood, and placement of internal rebars, among other factors. It’s also possible to visualize the geometry of the different types of vibration, called Chladni patterns, that are possible in a violin via a Chladni plate.

A photograph of a violin-shaped aluminum Chladni plate showing a Chladni pattern. Image by Stephen Morris — Own work. Licensed under CC BY 2.0, via Flickr.

How do Chladni plates work and how did they come about?

Ernst Chladni: Exploring Meteors and Music

We now know that sound propagates in waves through a solid, gas, or liquid medium — but we didn’t always know this. In the late 1700s, a German scientist named Ernst Chladni was the first to show that sound travels via waves by devising a way to visualize their vibrations.

Shortly after obtaining a law degree, Ernst Chladni made an abrupt career change that led him to become known as both the “father of meteoritics” and the “father of acoustics”. Chladni’s own father was a law professor and disapproved of his son’s interest in science, pressuring him to follow in his footsteps and become a lawyer. Chladni dutifully did what was expected of him, but shortly after graduating from law school in 1782, he received news of his father’s death. While this must have been a difficult time for Chladni, he felt free to pursue the career he actually wanted and turned his attention to physics.

Ironically, Chladni’s legal background gave him an advantage in this science: Having gained experience in reviewing eyewitness testimony for court cases, he used similar methods to support his theory that meteors are extraterrestrial rather than volcanic in origin, which was the prevailing consensus at the time.

Chladni researched all he could about objects falling from the sky and found people who witnessed the events and had heard and seen similar phenomena: masses of rock falling to the ground, fireballs, explosions, and sonic booms. After compiling the most reliable eyewitness reports, Chladni was able to estimate the speeds at which the rocks entered the atmosphere. He concluded that these extremely high speeds, in addition to the rocks’ scorched appearance, were only possible if the rocks came from outer space.

Left: Ernst Chladni. Image in the public domain in the United States, via Wikimedia Commons. Right: Illustration of the Chladni plate technique. Image in the public domain in the United States, via Wikimedia Commons.

Chladni also paved the way for experimental acoustics. It was perhaps the physicist’s interest and ability in music that inspired him to pursue the field, inventing new instruments based on inventions of Benjamin Franklin and Robert Hooke, including the euphone and the clavicylinder. He toured with his instruments across Europe, giving demonstrations and explaining the science behind their designs.

Among his achievements, he was able to determine sound velocities in gases using an organ pipe and developed Chladni’s law. This formula relates the frequency of modes of vibration for a flat circular plate. Among other applications, Chladni’s law can help predict patterns of vibration on flat surfaces and describe the vibration of cymbals and bells.

Chladni’s interest in music and acoustics led him to consider an instrument’s shape and symmetry, fostering the idea for which he is best known…

Finding the Art in Acoustics with Chladni Plates

Inspired not only by Robert Hooke’s instruments but also his experiments with visualizing nodal patterns, Ernst Chladni developed a technique of his own to show modes of vibration on a metal plate.

Here’s How It Works

The shape of a Chladni plate can be square, rectangular, circular, or even shaped like a violin or guitar body, as long as it has a fixed constraint at the center. (In Chladni’s case, he took a flat, rectangular metal sheet and secured it in the center to a sturdy base.) The plate is dusted with a material in order to see the patterns, such as flour, sand, or salt. (We used sand for our experiments!) Next, the plate is excited by drawing a violin bow across the side of the plate until it reaches resonance.

When the plate is excited, some areas vibrate and some areas don’t move. More specifically, you are able to see the standing waves along the nodal lines of the plate. The sand moves away from the antinodes, where the amplitude of the standing wave is maximum, and toward the nodal lines, where the amplitude is minimum, forming patterns known as Chladni figures.

Note: Turn down your sound before playing this video. The note generated by the Chladni plate is quite jarring, and not exactly music to your ears…

Depending on your level of dexterity, you can “play” a Chladni plate by holding the different nodes and exciting it with a bow at different antinodes. The distinct patterns change and vary, depending on the tone.

Many of these patterns are quite interesting:

Two Chladni figure patterns on the same plate in different modes.

We’ve seen how the patterns on a Chladni plate are created, but what do they mean?

All objects, including Chladni plates, have a set of natural frequencies at which they vibrate. A system, such as standing waves in a musical instrument, tends to vibrate at certain discrete frequencies called natural frequencies or eigenfrequencies. Once vibrating at a certain frequency, a structure deforms into a corresponding shape: the eigenmode.

The first six eigenmodes of a simply supported rectangular plate.

A plate is a continuous system that shows eigenfrequencies that depend on geometry, material properties, and constraints. The number of eigenfrequencies it can exhibit is infinite. The modes that are excited enough to make an impact are especially of interest. A plate’s natural frequencies depend a lot on shape and support conditions on the edges of the geometry, as well as its bending stiffness. In instrument production, for example, eigenmode frequencies measured in hertz relate to the stiffness of the wood.

A representation of Chladni patterns on a guitar plate. Compare the left image at a lower frequency (109 Hz) with the right image at a higher frequency (426 Hz).

“Seeing” Sound with Structural Mechanics Simulation

Visualizing sound has applications in many areas, such as furniture placement in a room and analyses of fluid-filled pipes. Visualizing sound can even help building engineers design a concert hall so the acoustics of the building don’t interfere with the violinist’s masterful rendition of Paganini’s Caprice No. 24. By studying sound’s variations, wave forms, wavelengths, speed, and other properties, we can better understand how to manipulate and reproduce sound, as well as account for its physical effects in designs.

An example of a Chladni plate model.

Structural analysis software enables you to simulate the properties of structural vibrations in plates, shells and membranes — with a Chladni plate as a basic example for doing so. The Structural Mechanics Module, an add-on product to the COMSOL Multiphysics® software, includes functionality that makes it easy to set up a plate geometry in a variety of shapes and account for a fixed constraint in the center. You can choose the plate material, usually either steel or aluminum, from the available selection in the Material Library.

The COMSOL® software also includes predefined physics settings for running an eigenfrequency study. Results from this study show the Chladni figures that form at different frequencies. As shown below, the patterns formed at 610 Hz vary greatly from the patterns formed at 3815 Hz. The analysis of sound waves at the different frequencies of a Chladni plate can be applied to other design projects involving the physical effects of sound.

Chladni simulation at 610 Hz (left) vs. 3815 Hz (right).

Taking the functionality a step further, a COMSOL Multiphysics model of a Chladni plate can be transformed into a specialized user interface called an app. The simulation specialist can build an app with restricted inputs and outputs from the simulation for ease of use. This way, people without simulation expertise still have a way to visualize the Chladni patterns and experiment with the parameter changes, without having to figure out the underlying model.

A screen recording of the Chladni Plate app.

Applications of Chladni Plates Beyond Sound

While many methods of visualizing sound have replaced Chladni’s technique, scientists still see its potential for studying physics phenomena. For instance, physicists tend to agree that the particle motion of nodal lines is random and therefore can’t be controlled — but researchers have shown that the motion of multiple objects could be controlled on a Chladni plate. One research team used a laser light instead of a violin bow to excite a thin, rigid membrane, and observed a similar effect with small vibrating objects. They then visualized the patterns through an array of quantum dots. This discovery could lead to a device that can detect small gravitational anomalies when designing shielding for nuclear materials.

Whether you’re interested in studying sound waves for multiphysics applications or designing a violin worthy of a standing ovation, Chladni plates are a way to observe the effects and distinct vibrational patterns of different frequencies — thus enabling us to “see” sound.

Next Steps

Try visualizing Chladni patterns yourself. We created an app specifically for this blog post and made it available to you in the Application Gallery. Note that you will need a COMSOL Access account and valid software license to download the app file.

Further Reading

• Check out these blog posts on further musical applications of simulation:
  • Teaching Students About Acoustics Phenomena with Apps
  • Can We Hear the Shape of a Drum?
  • Finding Answers to the Tuning Fork Mystery with Simulation
• Read about recent research into Chladni plates:
  • P.H. Tuan et al., “Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers“, The Journal of the Acoustical Society of America, vol. 137, no. 4, pp. 2113–2123, 2015.

File Formats for Printed Circuit Board Fabrication Data

In the early days of PCB design, we had to manually create photomasks for the copper layers by laying out shapes for traces and pads on clear sheets — for example, by using self-adhesive tape or rub-on shapes. Nowadays, the layouts for photomasks are created in ECAD design software and the fabrication data is transferred digitally to the manufacturer.

Before ECAD design software, photomasks had to be manually created in order to design PCBs. Image by Peellden — Own work. Licensed under CC BY-SA 3.0, via Wikimedia Commons.

There are several file formats for this purpose, and the ECAD Import Module supports one of the most widely used options: the ODB++® format. ODB++® format is a compressed archive of the various files that contain PCB fabrication data. Another widely used format in the industry is the Gerber format, which is supported for import into the COMSOL Multiphysics software through the conversion software NETEX-G, available from Artwork Conversion Software, Inc.

The New Kid on the Block: IPC-2581

A recent addition to the available file formats for PCB fabrication data is the IPC-2581 format, which was introduced in 2004. Maintained and developed by the IPC-2581 Consortium, the format is an open standard that defines a single XML-based file to contain all necessary information for the PCB fabrication. This information includes the copper layouts, layer stack-up and drill information, electrical connectivity and component data, the bill of materials, and other data. While IPC-2581 is still young when compared to the other major formats (the original Gerber format was introduced in 1980 and the original ODB++® format in 1995), we have seen it gain acceptance and support from both ECAD design software and PCB manufacturers.

While it is not yet possible to import IPC-2581 files via the ECAD Import Module (as of publishing this blog post), COMSOL has recently joined the IPC-2581 Consortium and support for the IPC-2581 format can be expected in a future version of the COMSOL software.

Editor’s note, 8/17/18: The ECAD Import Module supports the import of the IPC-2581 PCB format as of version 5.3a of the COMSOL Multiphysics® software.

Generating the PCB Geometry from the Layout Data

Regardless of the file format of the fabrication data, the 2D copper layout from a data file is reminiscent of the clear sheet with the attached shapes used in early design methods. The difference is that instead of a real “collage”, the designer creates a digital collage of shapes that builds up the traces and pads on the layer.

During the import, the first steps of generating a geometry for simulation with COMSOL Multiphysics are to import the individual shapes from the layout data and then combine them into connected geometric objects. During this process, interior edges are automatically eliminated to reduce the complexity.

The figure to the left shows circular shapes representing pads and rounded rectangles representing the copper traces in the ODB++® file. To the right, the same region of the layout is shown after the generation of a geometry without interior edges. The file is provided through the courtesy of Hypertherm, Inc., Hanover, NH, USA.

The resulting objects can still contain short edges, for example, if the imported data contains segmented circular edges. We can easily eliminate these by using the Remove Details operation, which can automatically find short edges and either collapse them or merge them if the requirement for tangency is fulfilled.

The segmented edges of a hole in a copper layer in the image to the left are joined together in the image to the right after applying the Remove Details operation, which can automatically detect and merge these segments. The file is provided through the courtesy of Hypertherm, Inc., Hanover, NH, USA.

By getting rid of these short edge segments, we gain better control over the meshing process. The mesh elements no longer have to respect the points between the edges. Instead, we can freely adjust the mesh element size to let the mesh elements resolve the hole boundary of choice.

When selecting an ODB++® file for import, the layer thickness and elevation information is read from the file and displayed in the Settings window for the import. We can edit this data and even import it from a previously saved text file. During the import, the selected 2D copper, dielectric, and drill layers are extruded according to this information. It is easy to turn off the extrusion of the copper layers by changing the Type of import setting to Metal shell from the default Full 3D. This can come in handy for simulations for which the copper layer can be modeled as a shell geometry. You will not have to spend time changing the individual thickness values to zero.

A partial view of the two-layer PCB geometry. The file is provided through the courtesy of Hypertherm, Inc., Hanover, NH, USA.

Use Selections for Faster Model Setup

PCBs are usually built up by many copper and dielectric layers. Setting up physics is quite tedious if we have to manually select geometric entities when setting up the simulation, for example, to assign a certain mesh size to some of the copper layers that consist of many faces. To make this process more efficient, the import defines selections for the different layers. These selections are available both for downstream geometry operations and for defining materials, physics, and even mesh settings.

Selections defined by the Import operation appear automatically in the Settings window for a Size attribute in the meshing sequence.

Try It Yourself

The ECAD Import Module includes a new tutorial model called Importing and Meshing a PCB Geometry from an ODB++® Archive. The model shows how to import data from an ODB++® file, generate the geometry of the PCB, and set up a mesh. Layouts imported with the ECAD Import Module can be used for any type of analysis in COMSOL Multiphysics: electromagnetics, structural, acoustics, heat, fluid flow, chemical, or combinations of these. Give it a try!

Support for implementation of the ODB++ Format was provided by Mentor Graphics Corporation pursuant to the ODB++ Solutions Development Partnership General Terms and Conditions (http://www.odb-sa.com/). ODB++ is a registered trademark of Mentor Graphics Corporation.

The Complex Nature of Threaded Geometries

Let’s say you just finished creating a CAD assembly of a fitting for the threaded steel pipe referenced above. Now, you want to analyze stress in your assembly in order to better understand how this portion of the pipe system performs. With our LiveLink™ interfacing products, you can perform such analyses by integrating the COMSOL Multiphysics® software into your design workflow.

Threaded pipes are common in fire sprinkler systems. Image in the public domain, via Wikimedia Commons.

Threaded geometries include a large number of details. The complex nature of these CAD assemblies causes additional preprocessing work and takes up more computing resources during analysis. One solution is to assume that the thread is symmetric and compute the solution in a 2D section cut from the 3D object.

In previous versions of the COMSOL® software, selections from the original geometry had to be manually redefined after synchronization — a process that can be time consuming. Thanks to improvements in version 5.3, setting up CAD assembly selections is now a more efficient process. All of the relevant selections are automatically loaded and properly assigned in the COMSOL Multiphysics environment. This makes it possible to run parametric studies as well as improve 3D designs from 2D analyses.

Want to see a firsthand example? Good news: There’s a new tutorial model in the Application Gallery that highlights this functionality.

Note: While today’s example uses LiveLink™ for SOLIDWORKS®, this functionality is also available for LiveLink™ for Inventor®. For more details, see the 5.3 Release Highlights page.

Performing a Reduced Stress Analysis of a Threaded Pipe Fitting

In this example, you can synchronize a full threaded pipe fitting geometry built in SOLIDWORKS® software into the COMSOL Desktop® environment via LiveLink™ for SOLIDWORKS®. To compute a reduced stress analysis, you obtain a 2D section from the 3D geometry via the Cross Section node. The analysis assumes that a torque of 5000 Nm is applied to the male thread part (shown below). This part is made up of the same steel material as the other parts in the design.

Left: Full 3D assembly synchronized in COMSOL Multiphysics. Right: 2D section cut for the stress analysis.

To compute the force transmission between each part of the assembly, the model uses structural contact. In SOLIDWORKS® software, these contact surfaces are defined as face selections. After synchronizing the assembly, all of the selections are automatically transferred over to the 2D axisymmetric model. This simplifies the process of setting up the contact pair, as it is no longer necessary to manually and individually select boundary entities in contact with one another. In particular, when it comes to the thread, you only need to create a selection for two surfaces in SOLIDWORKS® software instead of selecting fifteen edges in the 2D axisymmetric model.

Looking at the results of our stress analysis, we can see the von Mises stress when the maximum torque (5000 Nm) is applied. The plot indicates that the maximum value of stress is less than that generally reported for using a class 10.9 alloy steel, highlighting the potential of using this material in this pipe fitting design.

Simulation plot depicting the von Mises stress with the maximum applied torque.

In version 5.3 of the COMSOL® software, you can combine your complex CAD assemblies and COMSOL Multiphysics analyses for an efficient modeling workflow.

Ready to try this tutorial yourself?

SOLIDWORKS is a registered trademark of Dassault Systèmes SolidWorks Corp.

Autodesk, the Autodesk logo, and Inventor are registered trademarks or trademarks of Autodesk, Inc., and/or its subsidiaries and/or affiliates in the USA and/or other countries.

Taking a Closer Look at Tricycles

I tend to associate tricycles with children and picture them as small, brightly painted toys that are built more for enjoyment than practicality. However, tricycles are also a sustainable method of passenger transport and can even be used to transport bulk loads.

This application inspired the United Parcel Service (UPS) to use electric tricycles to deliver packages in Portland, Oregon, as well as other parts of the world. Although tricycles can’t carry as much as a typical UPS van, they are an alternative to emission-heavy vehicles and also help delivery drivers avoid traffic.

Tricycles can be used for many purposes, such as transporting loads and passengers. Left: Image by Gary J. Wood — Own work. Licensed under CC BY-SA 2.0, via Flickr Creative Commons. Right: Image by Pedro Szekely — Own work. Licensed under CC BY-SA 2.0, via Flickr Creative Commons.

We can use simulation to study a tricycle’s structure and ensure that it meets safety requirements. As an example, let’s consider a MUR-A tricycle developed by researchers from the Costa Rica Institute of Technology. To detect and address possible weak points in the tricycle’s design, the team used the Structural Mechanics Module with COMSOL Multiphysics to evaluate the mechanical performance of its frame. This enabled the team to find faults in the early stages, thereby optimizing the tricycle’s design before creating a physical prototype.

Studying an Aluminum Tricycle Frame with Structural Mechanics Analysis

The research team’s model consists of an aluminum 6063-T83 tricycle frame that uses steel 4130 for the handlebars and bottom bracket. As we can see in the following schematic, the frame is made of standard tricycle parts and includes a rear passenger or load zone. The team imported the 3D tricycle frame design into COMSOL Multiphysics using the CAD Import Module.

Tricycle components (left) and mesh (right). Images by A. Rodríguez, B. Chiné, and J. A. Ramírez and taken from their COMSOL Conference 2016 Munich paper.

To analyze their design, the researchers applied loads to different areas of the geometry. While the frame is the only tricycle part modeled, the team used other parts — seat tube, fork, handlebar, etc. — to define the loading conditions. These conditions include:

• Impact force (light blue)
• Pushing and pulling on the handlebars (gray and orange)
• Pedaling force on the bottom bracket (yellow)
• Driver’s weight (blue)
• Passenger’s weight (green)

The locations of the various loads applied to the geometry. Image by A. Rodríguez, B. Chiné, and J. A. Ramírez and taken from their COMSOL Conference 2016 Munich poster.

Using different combinations of the loading conditions, the team studied three distinct loading cases, shown in the table below. You can easily combine several sets of loads in COMSOL Multiphysics by using load groups and load case superpositions.

In regards to the horizontal impact case, it represents a sudden impact against a wall and assumes that the driver is removed from their seat while the passenger remains on the tricycle. As such, this case only accounts for the impact force and the passenger’s weight.

For each of these loading cases, the team performed a simple evaluation of the model’s stress and deformation distributions, enabling them to identify design issues and develop a safer tricycle.

Checking for Critical Areas in a Tricycle Frame Design

Overall, the simulation results show that in every loading case, there are regions in the tricycle frame design that are susceptible to stresses above the tensile yield strength of 214 MPa and the fatigue limit of 69 MPa. The researchers did not analyze the horizontal impact case for fatigue strength, as this is not (hopefully) a continuous condition.

In the steady-state pedaling case, there are critical areas that exceed the material’s elastic limit, located where the seat and horizontal tubes meet. This is expected, as the rider’s weight causes compression in these areas. Other areas of concern are the places where the horizontal tube and down tube intersect with the cage.

The steady pedaling case. Red indicates the areas where the von Mises stresses are greater than the material’s elastic limit (left) as well as the areas that are stressed more than the material’s fatigue limit resistance (right). Images by A. Rodríguez, B. Chiné, and J. A. Ramírez and taken from their COMSOL Conference 2016 Munich paper.

As for the fatigue evaluation in this scenario, one area (extending from where the seat and down tube meet to the front of the frame) fails when exposed to a static load behind the seat tube. This static load is a potential source of fatigue failure, since it is sometimes active and sometimes not.

There are similar weak areas where the horizontal and down tubes intersect with the cage. The results indicate that additional critical areas are located at the unions of the reinforcement tube, the cage area before the rear axle, and the intersection of the head and down tube.

The acceleration loading case has the same fatigue areas as the steady-state case, but spread over a smaller area. However, there is one difference. The intersection of the head and down tubes has a critical area that is slightly larger than the steady pedaling case, extending to the bottom of the down tube.

The acceleration case. Red indicates the areas that are stressed more than the material’s fatigue limit resistance. Image by A. Rodríguez, B. Chiné, and J. A. Ramírez and taken from their COMSOL Conference 2016 Munich paper.

The team then investigated the horizontal impact case. When comparing their numerical results with the material’s elastic limits, they saw that although the frame can withstand these loads, there are critical areas in the cage.

Examining the frame’s fork region for this loading case, the team saw that it behaves similarly to the frame as a whole. The results show that when the fork is exposed to the impact force, there are only a few deformation areas, shown in the following image. Despite this, the fork region may need to be redesigned, since it does not hold up under a fatigue analysis.

The fork region for the horizontal impact case. Red indicates the areas where the von Mises stresses are greater than the material’s elastic limit. Image by A. Rodríguez, B. Chiné, and J. A. Ramírez and taken from their COMSOL Conference 2016 Munich paper.

Next Steps for Studying a Tricycle Frame’s Mechanical Performance

Through their work, the researchers gathered helpful insight into the mechanical performance of their tricycle frame design. For instance, the simple fatigue analyses show that while most of the frame withstands static loads, it is compromised when it comes to long-term durability. As such, the tricycle frame needs to be strengthened.

According to existing research, one way to improve this design is to combat the tricycle frame’s low fatigue life by changing the material from aluminum 6063, with a fatigue limit of 69 MPa, to aluminum 6061-T6, which has a higher fatigue limit of 96 MPa.

While the simple analyses discussed today are a good starting point for improving the tricycle frame design, further studies (such as more fatigue and impact simulations) are required. Through this, the researchers can fine-tune their tricycle frame design, ensuring the safety of riders and passengers.

Further Reading

• Take a look at the researchers’ full paper: “Finite Element Modeling of an Aluminum Tricycle Frame“
• Browse the structural mechanics category on the COMSOL Blog

Developing Sensors with Higher Bandwidths for Accelerometers

There are a number of industries that rely on accelerometers. Take automotive designers, for instance, who often use these electromechanical devices to analyze shock and vibrations in safety testing. In addition, the developers of consumer electronics use these devices as a means of detecting orientation in digital cameras and tablet computers.

Automotive safety testing is just one application of accelerometers.

To detect the size and direction of an object’s acceleration, accelerometers feature sensor packages. Together, the components of these packages determine the frequencies for which the accelerometer provides accurate measurements. For example, modern commercial products typically feature a bandwidth of 10 to 20 kHz. As technologies continue to evolve and higher frequencies need to be measured, sensor packages must be able to handle higher bandwidths.

Recognizing this, a team of researchers from the Fraunhofer Institute for High-Speed Dynamics, Ernst-Mach-Institut, EMI, and the Albert-Ludwigs-Universität Freiburg used the COMSOL Multiphysics® software to design and analyze a sensor package for a high-g accelerometer. At the heart of the design is a novel piezoresistive sensor chip, one that can measure transient accelerations up to 100,000 g. Compared to today’s state-of-the-art sensors, this piezoresistive sensor’s figure of merit (sensitivity multiplied by resonance frequency) is around an order of magnitude greater.

Using COMSOL Multiphysics® to Design and Analyze a Sensor Package for a High-G Accelerometer

To begin, let’s look at the design of the piezoresistive sensor chip. It includes:

• A stiff frame
• A bending plate
• Four piezoresistive elements, interconnected through a Wheatstone bridge

The sensor chip. Image by R. Langkemper, R. Külls, J. Wilde, S. Schopferer, and S. Nau and taken from their COMSOL Conference 2016 Munich paper.

In COMSOL Multiphysics, this configuration is fully modeled as a silicon MEMS device.

For the package itself, three of these chips are integrated onto a single ceramic plate. Oriented at right angles to one another, the chips are sensitive in the x-, y-, and z-directions.

The sensor — its package included — acts as a complex mass spring system. Bending in the plate as a result of acceleration causes the piezoresistive elements to stretch and compress, which in turn produces changes in electrical resistance.

The complete sensor package. Image by R. Langkemper, R. Külls, J. Wilde, S. Schopferer, and S. Nau and taken from their COMSOL Conference 2016 Munich paper.

While the researchers tested multiple sensor package designs, we focus on one specific example here. The geometry for this sensor package, shown below, was imported into COMSOL Multiphysics® via LiveLink™ for Inventor®.

Each color represents the following:

• White: package box and cap
• Red: ceramic plate
• Gray: piezoresistive sensor chips
• Orange: grouting
• Green: adhesive layers
• Blue: cable dummy

The example sensor package design with its cap lifted (a) and an expanded view (b). Image by R. Langkemper, R. Külls, J. Wilde, S. Schopferer, and S. Nau and taken from their COMSOL Conference 2016 Munich paper.

To analyze the sensor’s behavior over a specific frequency range, the researchers used two approaches:

1. Modal analysis of the system
2. Simulation of the sensor with an oscillating acceleration load applied between a frequency range of 0 to 250 kHz

The first approach provides the value and shape of the resonance frequencies, while the latter depicts the stress and displacement of components within the sensor package. This information is used to determine the relative resistance of the piezoresistive bridges as well as compute the output signals of the sensor chips.

Evaluating the Simulation Results

The simulation results shown here correspond to the following sensor package design parameters:

Let’s look at the sensor’s output signal for the frequency range of 0 to 250 kHz. Note that this signal is computed for 100,000 g and a supply voltage of 1 V. Further, a limit of 5% is defined with regards to the sensor’s maximum change in sensitivity.

Output signal for the sensor at various excitation frequencies. The plot on the left shows the whole frequency spectrum, while the plot on the right shows a close-up view of 0 to 100 kHz. Images by R. Langkemper, R. Külls, J. Wilde, S. Schopferer, and S. Nau and taken from their COMSOL Conference 2016 Munich paper.

From the plot on the left, it initially appears that the curve’s behavior is flat until about 130 kHz. But with a closer view, shown in the plot on the right, the sensitivity changes are also visible at lower frequencies. With the 5% limit in place, the potential bandwidth of the sensor package is 47 kHz.

The sensor package modes are also analyzed, specifically those shown as peaks in the frequency spectrum. As highlighted in the previous plot, the first mode, or “cap mode”, occurs at 39 kHz and has minimal influence on sensitivity. Aside from the cap oscillations, the first mode, or “package mode”, occurs at 128 kHz. This mode, which is also highlighted above, has a significant effect on the output signal.

Left: The first cap mode, deflecting in the z-direction. Right: The first package mode, oscillating in the y-direction. Images by R. Langkemper, R. Külls, J. Wilde, S. Schopferer, and S. Nau and taken from their COMSOL Conference 2016 Munich paper.

From the modal analysis, an additional oscillation is observed at 287 kHz. As the main source of displacement for the sensor element, this mode is expected to have the most influence on the sensor’s signal. To test this assumption, the researchers turned to experimental tests.

Main displacement mode inside the sensor element. Image by R. Langkemper, R. Külls, J. Wilde, S. Schopferer, and S. Nau and taken from their COMSOL Conference 2016 Munich paper.

Verifying Results with Experimental Data

When adapting the simulation study to the experimental phase, the researchers used the following parameters. For practical reasons, these parameters differ slightly from those used in the model.

An additional simulation study helped to predetermine the ranges of expected frequencies:

• 5% limit: 16 to 30 kHz
• Package mode: 67 to 98 kHz
• Sensor element mode: 129 to 200 kHz

In the experiment, a small glass hammer stimulates the sensor oscillation in order for the researchers to measure the eigenfrequencies. A sampling rate of 10 MHz is used to record the sensor’s impulse answer.

Impulse answer of the sensor to an oscillation. Image by R. Langkemper, R. Külls, J. Wilde, S. Schopferer, and S. Nau and taken from their COMSOL Conference 2016 Munich paper.

To examine the impulse answer for relevant frequencies, the signal is converted into the frequency domain. As indicated below, multiple peaks appear at higher frequencies. The highest peak at 930 kHz represents the first eigenfrequency of the actual sensor chip. The lower frequencies, up to about 70 kHz, are a portion of the excitation impulse.

Left: Impulse answer of the sensor from 0 to 2 MHz. Right: Impulse answer of the sensor from 0 to 350 kHz. Images by R. Langkemper, R. Külls, J. Wilde, S. Schopferer, and S. Nau and taken from their COMSOL Conference 2016 Munich paper.

Something interesting to note is the peak that appears at 153 kHz. This represents the sensor element’s oscillation that is expected between 129 and 200 kHz. This finding supports the theory that this oscillation has the biggest influence on the sensing element.

In the sensitivity analysis, an acceleration of 8600 g is applied to each axis. A titanium Hopkinson bar is used to produce the shock load, with an attachment included to ensure equal distributions of the load on each sensor axis.

The attachment for the Hopkinson bar. Image by R. Langkemper, R. Külls, J. Wilde, S. Schopferer, and S. Nau and taken from their COMSOL Conference 2016 Munich paper.

The measured output signals, shown in the plot below, are used to compute the sensitivities of the different axes. The expected sensitivity is 1.3 µ V/V/g, with a potential maximum deviation of 30%. The greatest deviation in sensitivity occurs at the x-axis (around 23%), while the other axes have much lower percentages. Note that all of the sensor chips fall within this deviation range.

The measured output signals under a load of 8600 g. Image by R. Langkemper, R. Külls, J. Wilde, S. Schopferer, and S. Nau and taken from their COMSOL Conference 2016 Munich paper.

These findings show good agreement with the expected values from the simulation results, further highlighting the suitability of the sensor package design for a high-g accelerometer.

Learn More About Analyzing and Optimizing Sensor Designs

• Read the full COMSOL Conference paper:
  • Development of a Package for a Triaxial High-G Accelerometer Optimized for High Signal Fidelity
• Explore the role of simulation in analyzing and improving other sensor designs:
  • Simulating a MEMS-Based Pressure Sensor Inspired by a Cave Fish
  • Simulating a 3D Multilayered Graphene Biosensor Design
  • Designing CSRR-Based Sensors to Monitor Chronic Kidney Disease

Autodesk, the Autodesk logo, and Inventor are registered trademarks or trademarks of Autodesk, Inc., and/or its subsidiaries and/or affiliates in the USA and/or other countries.

Exploring the Beam Section Calculator

You can use the Beam Section Calculator as a utility tool to accurately compute a beam section’s properties and stress distribution or as a complement to a beam element model. This app can be downloaded with the Structural Mechanics Module, an add-on product to the COMSOL Multiphysics® software. There are two versions of the Beam Section Calculator. The first version uses only the Structural Mechanics Module, while the second version also uses LiveLink™ for Excel®.

While the first version of the app has a fixed amount of section data, the second version enables us to replace the section data list with a workbook in Excel® spreadsheet software. This process is explained further in this blog post.

The user interface of the Beam Section Calculator with LiveLink™ for Excel®.

The Beam Section Calculator provides data for about 9000 beam sections from American and European standards. The table below shows a few of the available beam section types.

In the Designation section of the app, we choose the beam type through a multilevel sequence of steps. When we choose a beam standard, it updates the list of beam shapes. This in turn affects the beam types, as there are different types available for each shape. Once we’ve selected a type, we pick the beam designation from the look-up table, shown below, and make the beam units either imperial or metric.

The Designation section, where we select the desired beam section.

The beam section geometry parameters are automatically updated in the Dimensions section, shown in the image below. To provide a visual of how the beam geometry looks, this section shows a sketch of its dimensions. We can also view a geometry with the appropriate scaling in the Graphics window on the left side of the app.

The beam geometry parameters in the Dimensions section.

Calculating the Beam Section Properties

In a computational structural analysis, beams are usually depicted with lines representing the center line. Instead of representing the cross section in the geometry, these specific elements use properties like area and moments of inertia. The Beam Section Calculator provides us with an accurate evaluation of these section properties.

After selecting the desired beam section, we click on the Compute button to get the section properties. The results are displayed in the Section Properties tab.

The only section property actually stored in the app is a minimum set of the sections’ geometrical dimensions; all of the other data is computed. For this reason, the tabulated values may differ somewhat from what is seen in a sheet from a beam manufacturer. The cross-section data computed in the app is exact, whereas values found in tables are usually based on approximate formulae.

The computed section properties.

The beam section properties computed in the app are the properties used in the Beam interfaces and found in the Section Properties section. They account for the main properties that characterize a structural beam, including:

• Cross-section area (A)
• Coordinates of the center of gravity (xG and yG)
• Principal moment of inertia, largest (I1) and smallest (I2)
• Direction of the principal axes (alpha)
• Distance to shear center in principal directions (e1 and e2)
• Torsional constant (J)

For xG and yG, we can specify the reference point from which we want to evaluate these coordinates. No need to compute the solution again; we just click on the Evaluate values button. Regarding the direction of the principal axes, their orientations are given by the principal moment of inertia. Alpha corresponds to the angle between the global x-axis direction and the first principal axis (given by the largest principal value). As for the shear center, also known as the center of rotation, it is the point around which the shear stress from bending has no torque.

In addition, the Section Properties tab shows the stress evaluation properties, including:

• Section height in principal directions (h1 and h2)
• Torsional section modulus (Wt)
• Maximum shear stress factor in principal directions (mu1 and mu2)

The app also computes the shear correction factor in the principal direction (kappa1 and kappa2). This is a multiplier that makes the strain energy from the average shear stress and shear strain of the cross section equal to its true shear energy. We need this value when modeling shear flexible beams using the Timoshenko beam theory.

We can use the properties listed above in the Beam interfaces by clicking on the Save button to store the data in a text file. Uploading this file into COMSOL Multiphysics enables us to define the variables, which in turn helps us describe the cross-section data settings.

Computing Stress with the Beam Section Calculator

When using beam elements, the stresses computed are conservative, only considering the worst case of stress interaction. This is because we don’t know the actual geometrical shape of the cross section, only its properties (as described above).

The Beam Section Calculator uses the true section geometry of the beam, including any fillets. With a set of section forces, it is thus possible to accurately compute the stress distribution within the section.

In Input forces, we enter the set of forces to be used in the stress evaluation.

The Input forces section.

To set the forces after calculating the section properties, we simply update the stress in the Graphics window by clicking on the Update plot button. In addition, we can specify a maximum allowable stress, to which the app compares the effective stress. If the stress is above the allowable specified value, it displays a warning message.

To visualize our results, there are a few plots that we can choose from. Bending Moment plots the bending stress caused by a moment around the principal axes. This option also shows the orientation of the principal axes. The coordinate system of the principal axes is located at the section’s center of gravity.

The bending stresses from moment around 1-axis (left) and 2-axis (right).

Shear Force displays the shear stress caused by a shear force along the principal axes. The surface plot shows the shear stress resultant, while the arrow plot shows its orientation. In addition, the location of the shear center is shown as a red dot.

The shear stresses from a force along 1-axis (left) and 2-axis (right).

Torsion plots (as shown below on the left) show the shear stress caused by a twisting moment. As with the Shear Force plot, the surface plot displays the shear stress resultant, while the arrow plot shows the orientation. Effective Stress plots (as shown below on the right) show the von Mises stress (MPa).

Additionally, Warping, shown below, plots the out-of-plane deformation caused by torsion.

Replacing the Beam Section Data with LiveLink™ for Excel®

When using LiveLink™ for Excel®, we can manually edit the list and dimensions of the beam section that we want to use. Clicking on the Replace sections button uploads the Excel workbook containing the new beam section data. This lets us add beams from another standard.

The contents worksheet in the beam section data file.

This workbook follows a specific format. First, it must contain a worksheet named contents, which provides the structure for the app’s interface. The first column defines how the beam is described in the Beam standard combo box. As for the second column, it contains the number of design parameters (up to three) that define the beam designation. For instance, an American beam is usually defined with two parameters (W 4×13), while a European beam typically only uses one parameter (HEA 100). This determines the number of list boxes in the designation section.

The third column describes the Beam shape combo box and should correspond with one of the generic beam geometry parts in the model, including:

• I-beam
• H-beam
• C-beam
• U-beam
• T-beam
• L-beam

In the fourth column and after, we enter the name of the beam section type. To specify the beam dimensions with a different unit system, we add the unit name to the section type, separating the names with an underscore.

For each beam section, the dimensions are stored in a separate worksheet. The name of the worksheet corresponds to the full description of the beam type, including the standard name, beam shape, and beam type, with each separated by an underscore. As an example, the worksheet name for a UPE European beam is European_U-beam_UPE.

A section-type worksheet in the beam section data file.

After the beam section data is replaced, the workbook is automatically stored in the .comsol/ directory. Every time the app starts, it asks whether we want to use this user-defined workbook or an embedded one. To avoid this notification, we can save the app and choose to embed the modified workbook. To get back to the original beam section data, we click on the Reset all button.

Coding for the Interface of the Beam Section Calculator

Let’s turn our attention to the inner workings of the Beam Section Calculator. This information is not necessary for using the app, but as with any app distributed with the software, it is interesting to look behind the scenes.

The app’s dynamic interface helps us to easily navigate through the multiple beam sections. After selecting a value in a combo box, the combo box that appears next automatically populates with the appropriate values.

Code for populating the combo box in the Beam Section Calculator.

The code above runs when we change the value in the Beam Standard combo box. Whether we choose a European or American option, the choice list shapeList is populated with the right values. String arrays define the list for each combo box when the app starts.

Code showing how the structure of the combo boxes is initialized.

The list box contains the design parameters used to define the beam geometry parts. The list of values is associated with a specific beam section type using a HashMap table. We can define this table as a utility class.

The HashMap table, created in the Application Builder as a utility class, associates string arrays with string inputs.

We can store a large amount of data this way as long as we don’t plan on replacing it. Or, we can use LiveLink™ for Excel® to read the data from a workbook embedded in the app. As this version of the app has a different structure, it allows the interface to be more flexible. It reads a workbook, which can be manually edited.

The readExcelFile() method enables the app to read the contents of a worksheet.

The readExcelFile() method transfers the data from an Excel workbook to a string in the app. The method then reads the worksheet’s contents, which contain the structure of the combo box. The geometry data for each beam type is stored in separate worksheets.

The Underlying COMSOL Multiphysics® Model

Now that we’ve explored the app itself, let’s discuss the underlying model. The Beam Section Calculator uses the Beam Cross Section interface, which is part of the Structural Mechanics Module, to analyze beam sections.

We can create a beam section geometry with a beam geometry part from the Part Library. Here, we find principal shapes for European and American standard beam sections as well as generic beam shapes. These geometry parts use multiple parameters to control all of the section’s dimensions, while the classical standard beams use designation parameters (for example, entering 10 and 15.3 as parameters gives a standard C10x15.3 beam cross section). The generic beam geometry part is fully parameterized so we can generate any section.

The beam geometries in the Part Library of the Structural Mechanics Module.

When selecting a beam in the app, it provides the geometry part with the corresponding input parameters. The version of the app with LiveLink™ for Excel® uses generic beam geometry parts. This enables us to easily redefine our own beam section.

Ready to try out the Beam Section Calculator app on your own? Click the button below to get started.

Further Resources

• Read more about using apps for structural analysis on the COMSOL Blog:
  • Efficiently Analyze Civil Engineering Designs Using an App
  • Connecting the Dots Between Theory, Model, and App
  • App: Analyze the Design of a Viscoelastic Structural Damper
• Watch a video that walks you through modeling structural mechanics in COMSOL Multiphysics

Excel is either a registered trademark or trademark of Microsoft Corporation in the United States and/or other countries.

Using Topology Optimization Results in the Design Workflow

Topology optimization is a useful capability because it can help us find designs that we would not have reasonably been able to think of ourselves. When developing a design, however, this is only the first step. It may not be reasonable or possible to construct a particular design found through topology optimization, either because the design is too costly to produce or it is simply not possible to manufacture.

Topology optimization results for an MBB beam.

To address these concerns, we can come up with new designs that are based on the results of topology optimization, and then carry out further simulation analyses on them. But how do we do this? As it turns out, COMSOL Multiphysics makes it simple to create geometries from the 2D and 3D plots of your topology optimization results, which you can continue to work with directly in COMSOL Multiphysics or export to a wide range of CAD software platforms.

Creating a Geometry from 2D Topology Optimization Results

To view topology optimization results that are in 2D, we can create a contour plot. Let’s use the Minimizing the Flow Velocity in a Microchannel tutorial to demonstrate this process. The goal of the tutorial is to find an optimal distribution of a porous filling material to minimize the horizontal flow velocity in the center of a microchannel.

First, we open up the model file included in the tutorial and go to the Contour 1 plot feature under the Velocity (spf) plot group.

The horizontal velocity (surface plot) and velocity field (streamlines) after optimization. The black contours represent the filling material.

In the above plot, the black contour is where the design variable, , equals 0.5. This indicates the border between the open channel and filling material. This is the result that we would like to incorporate into the geometry. In other applications, the expression and exact level to plot may differ, but the principle is the same: to find a contour that describes the limit between the solid and nonsolid materials (typically a fluid of some kind).

To create a geometry from this contour plot, we right-click the Contour feature node and choose Add Plot Data to Export. We need to make sure that we choose the data format as Sectionwise before we export the file.

The Sectionwise format describes the exported data using one section with coordinates, one with the element connectivity, and another that includes the data columns. It is important to note that the middle section, which describes how the coordinates of the first section are connected, will allow a contour plot with several closed loops or open curves.

The Spreadsheet export format is not suited for this particular use for several reasons, most importantly because it will assume that all coordinates are connected one after the other. This means that if there is more than one isolated contour, it will not be possible to build the Interpolation Curve feature. Also, the coordinates are scrambled, so the curve in the next step (discussed below) will not be drawn in the same way as seen in the contour plot.

To create the new geometry, we choose Add Component from the Home toolbar and choose a new 2D Component. Then, we copy the geometry feature nodes from the original geometry and paste them to the geometry sequence of the new 2D component. After this, we add an Interpolation Curve from the More Primitives menu on the Geometry toolbar and set the type as Open Curve, data format as Sectionwise, and a tolerance of 2e-2.

A smaller tolerance will give a curve that is more true to the data, but the outcome might be an intricate or “wiggly” geometry. In turn, a higher tolerance may give a curve that is too simplified and quite far from the optimized result.

Geometry with the interpolation curves representing the results of the topology optimization.

The geometry can now be used to run further simulations and to verify the created geometry within COMSOL Multiphysics.

Exporting 2D Geometries to CAD Software

The DXF format is a 2D format that most CAD software platforms can read. DXF also describes the higher-order polygons between the points, so it usually gives a better representation than exporting only the points.

To export the optimized topology from this geometry to a DXF file, we can follow the steps below. Please note that there is an optional step for if you only want to include the shape of the optimized topology in your DXF file.

1. Add a Union from the Booleans and Partitions menu on the Geometry toolbar
2. Include all of the objects
3. Use a Delete Entities feature to remove the unwanted domains (optional)
4. Click the Export button on the Geometry toolbar to write to the DXF format for a 2D geometry

Now, let’s see what to do when working with topology optimization results that are in 3D.

How to Generate a Geometry of 3D Topology Optimization Results in COMSOL Multiphysics®

After performing a topology optimization in 3D, we usually view the resulting shape by creating a plot of the design variable; for example, an isosurface plot. We can directly export such a plot to a format that is compatible with COMSOL Multiphysics and CAD software and can even be used directly for 3D printing. This file format is the STL format, where the surfaces from the results plot are saved as a collection of triangles. It is a common standard file format for 3D printing and 3D scans in general.

In COMSOL Multiphysics, it is possible to export an STL file from the following plot features:

• Volume
• Isosurface
• Surface
• Slice
• Multislice
• Far Field

The software also supports adding a Deformation node on the plot feature, in case we want to export a deformed plot. The volume and isosurface plots are the most commonly used plot types for topology optimization, so we will focus our discussion on these two options.

To create an isosurface plot, we first add a 3D plot group to which we add an Isosurface feature node. In the Expression field, we then enter the design variable name, set the entry method as Levels, and fill in an appropriate value of the design variable representing the interface between the solid and nonsolid materials.

To demonstrate this process, let’s look at the example of the bridge shown below, where the optimal material distribution takes the familiar shape of an arch bridge. The optimization algorithm is maximizing the stiffness of the bridge subjected to a load to reach the displayed solution. To obtain the displayed isosurface plot, we use the expression 0.1 for the level of the design variable.

An isosurface plot of the 3D topology optimization for a deck arch bridge.

As you can see in the screenshot above, isosurface plots are not necessarily capped or airtight, so an exported volume plot may be a better choice, especially if we want to run further simulation analyses in COMSOL Multiphysics.

We can create a suitable plot by adding a Volume feature node to a 3D plot group. Then, we add a Filter node under Volume and set a suitable expression for inclusion. In this example, we use the expression rho_design > 0.1.

A volume plot of the deck arch bridge.

Exporting Plot Data in the STL Format

Exporting the data into an appropriate file format is simple. We right-click the Volume or Isosurface feature node and select Add Plot Data to Export. In the settings window of the resulting Plot node, we then select STL Binary File (*.stl) or STL Text File (*.stl) from the Data format drop-down list.

The exported STL file is readily readable by most CAD software platforms. To continue with the simulation of the geometry, import the STL file to a new COMSOL Multiphysics model, a process that we discuss in a previous blog post.

Summary on Creating Geometries from Topology Optimization Results

If you want to compare actual CAD drawings with your optimized results, you need to export the data in a format that can be imported into the CAD software you are using. The DXF format (for 2D) and the STL format (for 3D) are widely used formats and should be possible to import in almost any software platform.

In this blog post, we have discussed the steps needed to export topology optimization results in the DXF and STL formats. This will enable you to more efficiently analyze your model geometries within COMSOL Multiphysics and CAD software.

Further Resources

• Learn more about topology optimization and exporting geometries on the COMSOL Blog:
  • Finding a Structure’s Best Design with Topology Optimization
  • How to Use Acoustic Topology Optimization in Your Simulation Studies
  • How to Reuse a Deformed Shape as a Geometry Input

Integrating Simulation Apps and CAD Design Tools

For the design community, the advantage of creating easy-to-use and custom simulation apps is obvious. If simulation can be incorporated into the CAD design process, then products will move to market quicker, with lower risk of mistakes and anomalies that might arise in the manufacturing process. Furthermore, introducing simulation into the entire engineering workflow — as opposed to just a few specialists in analysis and simulation — increases a company’s scope for innovation while incorporating everyone’s expertise.

The Bike Frame Analyzer app, combining the benefits of simulation and CAD design.

Combining the power of a CAD design tool (in this case, the SOLIDWORKS® software) with a simulation app (the structural analysis of a bike frame) in the same modeling environment enables the simulation and/or design engineer to work with both in synchronicity. The associative features between the two tools means that changes applied within one of them are immediately updated in the other. While the Bike Frame Analyzer app is quite simple in its structure and is easy to use, it contains great flexibility in the parameters that can be investigated, whether they involve the design’s geometric dimension, material properties, or the loads and constraints to which the frame is subjected.

Exploring the Bike Frame Analyzer Simulation App

The Bike Frame Analyzer app enables you to apply a combination of loads and constraints to the frame geometry and identify the maximum stress location. You can also easily analyze different configurations of a frame to see the effects of varying dimensions and materials.

By building a customized user interface with the Application Builder (included in the COMSOL Multiphysics software), we can design the app to streamline our simulation workflow. For this app, the settings and feedback are placed in vertically arranged sections to the left; a large graphics display to the right shows the model geometry, mesh, and results; and the top ribbon contains all of the app’s buttons, which initiate a process in the simulation workflow (e.g., solving).

Apps that use the LiveLink™ for CAD products are designed to work side-by-side with the CAD tool you are using. This means you can run the Bike Frame Analyzer app while the original CAD file is open in the SOLIDWORKS® software and switch between the user interfaces as required.

The UI of the Bike Frame Analyzer app.

During the development process, we may come up with many iterations of the frame design, which leads to many versions of the design file. Therefore, the file information of the current model geometry along with the date and time of the last update are always displayed in the CAD design settings section. By default, the Use geometry from option is set to Specified document to ensure that we connect to the correct SOLIDWORKS® file during a geometry update.

The CAD design settings section displays the time of the last geometry update and file information about the design.

To analyze a new SOLIDWORKS® file, configuration, or display state of a design, we can select the Active document option from the Use geometry from list before updating the geometry. This is possible when we configure the new SOLIDWORKS® file with similar user-defined parameters and selections to the mountainbike_hardtail.SLDPRT file that is included with the app. We will discuss this in more detail later.

We can update the geometry in two different ways, depending on whether we would like the dimension values entered in the app to be sent to SOLIDWORKS® or vice versa. Clicking on the Update from App button results in the former. In SOLIDWORKS®, the frame geometry is regenerated according to the received dimensions and sent back to the app. The second option leaves the geometry unmodified in SOLIDWORKS®. When we click the Update from CAD button, the current dimensions and geometry from the SOLIDWORKS® file carry over to the app instead and are reflected in the updated values on the Dimensions tab of the Definitions section. This method is useful when making changes directly in SOLIDWORKS® or when analyzing a completely new frame design.

Next, let’s dive into the physics setup in the underlying bike frame model.

Defining the Physics for the Underlying Bike Frame Model

Even though our model only concerns the frame of a bike, we need to take into account that loads are applied to components that are attached to the frame. For example, the weight of the rider is distributed on the seat and handlebar and the force resulting from the front wheel hitting the curb is transferred to the frame through the fork. These components can be approximated as rigid bodies in this simulation, but it is important that we apply the loads in the correct locations so that their contribution to the moment can be calculated.

The perfect tool for setting up these loads is the Rigid Connector boundary condition, available in the Solid Mechanics interface in the COMSOL® software. This is a type of kinematic constraint that keeps the faces it applies to as if they would be attached to a rigid body. With the Rigid Connector boundary condition, we can also apply forces at specified locations. The force’s contribution to the moment is automatically taken into account. With the rigid body assumption of the attached components, the simulation becomes a virtual test rig for bike frames.

Screenshot of the COMSOL Multiphysics® software showing the Rigid Connector boundary condition, which is defined to constrain and apply the load on the fork.

As seen in the above figure, the fork’s load is applied to the rigid connector at its center of rotation, which is defined at the position of the front axle using the dimensional parameters for the frame synchronized from the SOLIDWORKS® design. The sketch below is included in the app to help the app users, who only need to enter the magnitude of the load and select the constraint that should be applied.

Settings for the load and constraint on the fork in the COMSOL® app.

Next, we’ll discuss how to implement the update of the SOLIDWORKS® geometry in the app.

Synchronizing Geometries with LiveLink™ for SOLIDWORKS®

The LiveLink™ for SOLIDWORKS® interface is the link between the geometry in the simulation app and the design in the SOLIDWORKS® software. In the model, this tool is represented by the first feature node in the geometry sequence, the LiveLink™ for SOLIDWORKS® node. In addition to the geometry, the LiveLink interface also keeps track and updates the dimensions and selections used for the physics boundary conditions. These are listed in the Settings window for the node and are important for setting up the simulation and changing the geometry from the app.

The geometry sequence of the model and the Settings window for the LiveLink™ for SOLIDWORKS® feature.

When a user clicks on either the Update from CAD or Update from App buttons in the app UI to update the geometry, a method is run that includes the command importData. This command corresponds to clicking on the Synchronize button in the Settings window for the LiveLink™ for SOLIDWORKS® node. In the Application Builder in COMSOL Multiphysics®, this command is in the synchronizeCAD method:

model.geom("geom1").feature("cad1").importData();

In the above command, the geom1 tag refers to the geometry sequence and the cad1 tag refers to the LiveLink™ for SOLIDWORKS® feature.

During synchronization, the interface also provides the file name, configuration, and display state of the synchronized CAD file. The file information is displayed in the Settings window of the LiveLink™ for SOLIDWORKS® feature. If the file has already been synchronized before, the interface ensures that the correct file and configuration is used as long as the CAD file is open in the SOLIDWORKS® software.

In the app, the synchronizeCAD method contains the commands where the synchronized file information is accessed. For example, the line

configuration = model.geom("geom1").feature("cad1").getString("configuration");

obtains the configuration for the synchronized design and assigns it to the string variable configuration.

In the same method, the command

model.geom("geom1").feature("cad1").set("synchronizewith", document_status);

configures the LiveLink™ for SOLIDWORKS® feature to synchronize either the previously synchronized file or a new file.

This is based on the setting of the document_status variable, which is tied to the Use geometry from combo box in the app’s UI. Valid values for the synchronizewith property are active and specified, where the former can be used to synchronize any file that is currently active in SOLIDWORKS®.

Connecting Model Parameters to the Frame Dimensions

We can update the bike frame dimensions in the SOLIDWORKS® file directly within the Bike Frame Analyzer app. To enable the update, each input field in the Dimensions tab in the app UI is connected to a global parameter in the model. These parameters are in turn connected via LiveLink™ for SOLIDWORKS® to global variables defined in the SOLIDWORKS® file. For example, the input field Head angle (A) has its source set to the LL_A global parameter, which we can find in the Model Builder in COMSOL Multiphysics® by going to the Global Definitions > Parameters node.

Parameters that start with LL_ are automatically generated and updated when needed by the LiveLink™ interface during synchronization. We can also find these parameters in the Settings window for the LiveLink™ for SOLIDWORKS® node, where the corresponding global variables in the SOLIDWORKS® file are also listed. For the LL_A parameter, the corresponding SOLIDWORKS® global variable is called A. In the SOLIDWORKS® UI, all user-defined global variables are in the Equations window.

Since a SOLIDWORKS® file may contain hundreds of dimension variables, both automatically generated and user defined, only those specifically selected are synchronized. Those that are synchronized are listed in the COMSOL Parameter Selection window, which we can open from the COMSOL Multiphysics tab in SOLIDWORKS®. In this window, we can also select new dimensional variables to include in the synchronization.

The COMSOL Parameter Selection window in the SOLIDWORKS® software. Parameters added to the lower table are synchronized.

Updating Parameters

Now that we have seen how the bike frame model’s parameters connect to the dimensions in the SOLIDWORKS® file, let’s take a look at the actual update process.

As already mentioned, we can update the geometry either based on the dimension values from the app or from SOLIDWORKS®, depending on which update button is selected. When the user clicks on the Update from App button, the frame dimensions change according to the values entered in the app interface. Under the hood, the synchronizeCAD method is run, particularly the command

model.geom("geom1").feature("cad1").importData();

This command, corresponding to the Synchronize button in the Settings window for the LiveLink™ for SOLIDWORKS® node, first sends the dimension values from the app to the SOLIDWORKS® software, where the corresponding user-defined global variables are updated, thus resulting in a rebuild of the geometry. After the rebuild is completed in SOLIDWORKS®, the geometry is sent back to the app.

During the second option for the geometry update, when the Update from CAD button is selected, both the app parameters and geometry are updated to reflect the current dimensions and geometry in SOLIDWORKS®. In this case, in the synchronizeCAD method, the command

model.geom("geom1").feature("cad1").updateCadParamTable(false, synchParam);

is run before the actual synchronization.

When the synchParam variable is set to true in the above command, the dimensional values retrieved from SOLIDWORKS® replace the parameter values in the app and are displayed in the app UI. During the subsequent synchronization, the SOLIDWORKS® geometry is not modified, since the dimension values in the COMSOL® app and the SOLIDWORKS® software are already the same.

Selections for Boundary Conditions

Assigning the appropriate geometric entity selections to the feature nodes in the underlying model is an important ability. These selections need to be maintained after changes to the CAD design, and even updated when an entirely new file is selected. One approach is to add selection input objects to the app interface in the Application Builder. This allows the user to inspect and make selections in the app after geometry updates. The Bike Frame Analyzer app, however, demonstrates a different approach, where the selections are made in SOLIDWORKS® using the selection functionality of LiveLink™ for SOLIDWORKS®.

The CAD file of the bike frame that is supplied with this demo app contains selections that have been defined on suitable faces to apply the boundary conditions. To view these selections, open the mountainbike_hardtail.SLDPRT file in SOLIDWORKS®. Then, on the COMSOL Multiphysics tab, click on the Selections button. The COMSOL Selections window that opens can be used to define selections.

COMSOL Multiphysics selections defined on the geometry in the SOLIDWORKS® software.

The selections are transferred to the COMSOL Multiphysics® software during a synchronization of the geometry and are listed in the Settings window for the LiveLink™ for SOLIDWORKS® node in the Model Builder. To view the selections, expand the Selections from CAD section. The selections are used as inputs to other operations further down in the geometry sequence. Finally, the output of those operations appears as the input selection for the rigid connector features in the Solid Mechanics interface in the COMSOL® software.

Setting up selections as outlined above makes it easy to work with the app. The LiveLink™ for SOLIDWORKS® interface takes care of the updates to the selections as the frame dimension is changed. Since the app relies on these selections being present in the model, there is code in the app to check that the selections exist after a geometry update. In the Application Builder, this code is included in the checkGeometry method:

String[] sel_CAD = model.geom("geom1").feature("cad1").outputSelection();

The command returns the list of selections transferred from the CAD file and stores it in the sel_CAD string array. Subsequent lines in the method compare the obtained selection names to the expected list and return an error if some are missing or incorrect.

System Requirements for Running COMSOL® Apps That Connect to CAD Software

We discussed one requirement for geometry updates: running the SOLIDWORKS® software with the CAD file open. In addition, SOLIDWORKS® needs to run on the same computer as the COMSOL client, where the COMSOL® app is open.

To synchronize geometries between CAD software and simulation apps, the CAD software and the COMSOL client need to run on the same computer.

The app itself runs on the COMSOL Server™ software, which can be installed on a remote computer, as illustrated above. The LiveLink™ for SOLIDWORKS® interface functionality for connecting to a CAD program comes with the COMSOL client, which can pass information to the app running on COMSOL Server™. However, working with any apps that require any of the LiveLink™ for CAD products is not supported in the web-based client.

Analyze Your SOLIDWORKS® Designs and CAD Files with the Bike Frame Analyzer App

To analyze your own frame design with the Bike Frame Analyzer app, you can add selections and global variables that make use of the same names.

First, set up user-defined global variables in SOLIDWORKS® with the same name as you find in the mountainbike_hardtail.SLDPRT app file. You also need to link these variables to the appropriate dimensions of the frame in the Equations window in SOLIDWORKS®. Next, enable the global variables for synchronization with the COMSOL Multiphysics® software from the COMSOL Multiphysics tab in SOLIDWORKS®. Click on the Parameter Selection button to open the COMSOL Parameter Selections window, where you can select all of the previously defined variables.

The last step of preparing the CAD file for synchronization is to define the selections with the names expected by the app. On the COMSOL Multiphysics tab in SOLIDWORKS®, click on the Selections button to open the COMSOL Selections window. Create new selections that are similar to those in the mountainbike_hardtail.SLDPRT file. Once finished, your design is ready for analysis with the Bike Frame Analyzer app.

Now that we’ve shown you how to analyze your own frame design, let’s see our Bike Frame Analyzer demo app in action…

Further Resources

• Browse the Video Gallery for a selection of tutorial videos on interfacing and app building:
  • Using COMSOL® Software with LiveLink™ for SOLIDWORKS®
  • Synchronize Parameters in COMSOL Multiphysics®
  • Using COMSOL® Selections in SOLIDWORKS®
  • Introductory Video Series on How to Use the Application Builder
• Check out the LiveLink™ for SOLIDWORKS® User’s Guide for more information on the interfacing product

SOLIDWORKS is a registered trademark of Dassault Systèmes SolidWorks Corp.

A Brief Introduction to Bolometers

The bolometer was first invented in 1878 by Samuel P. Langley, an American astronomer, with the intended use of studying solar irradiance and solar radiation intensity at different wavelengths. Bolometers consist of a strip of conducting material (a conducting absorber) that is thermally insulated from the rest of the device and mounted on a dielectric material, which acts as a heat sink and electrical insulator.

When a bolometer is exposed to incident electromagnetic radiation, the conducting absorber’s temperature increases in comparison to the rest of the device. As this temperature change occurs, the absorber’s electrical conductivity lowers, altering the flow of the bias current. This change in voltage is detected by a voltmeter and because the change is related to the amount of incident electromagnetic radiation, the device can be used as a sensor.

A schematic of a bolometer geometry that shows how the device operates. Image by J. Thomas, J.S. Crompton, and K.C. Koppenhoefer and taken from their COMSOL Conference paper submission.

The Many Applications of Bolometers

In recent years, the use of bolometers has extended to night vision cameras and astronomy as well as particle and nuclear physics. NASA, for instance, uses transition-edge sensor (TES) bolometers to sense minor changes that occur in temperature when photons are absorbed and converted into heat. These devices help generate detailed maps for astrophysics projects that illustrate the polarization of cosmic microwave backgrounds.

A bolometer array. Image by Geni. Licensed under CC BY-SA 4.0, via Wikimedia Commons.

Researchers at the Herschel Space Observatory are also utilizing bolometers. Their application relates to investigating distant galaxies and the beginning stages of star formation. Doing so involves using a device called the Spectral and Photometric Imaging Receiver (SPIRE), which consists of five arrays of bolometers. Bolometers are ideal in this case because they have the highest sensitivity for light in the far-infrared to millimeter range of any direct detector.

With their range of applications, bolometer designs need to be customized for different uses, while optimizing their overall sensitivity (a key design parameter). When it comes to measuring the design quality, it is favorable that bolometers are able to detect temperature changes of less than 0.0001°C.

AltaSim Technologies recognizes the importance of improving bolometer designs. With the help of COMSOL Multiphysics, they studied the impact of different design parameters on a bolometer’s sensitivity and the level of detection of incident electromagnetic radiation. Let’s see what they found…

Multiphysics Modeling Aids in the Optimization of Bolometer Designs

For their studies, the researchers noted that bolometer functionality is tied to three main physical phenomena:

• Heat transfer within the solid parts of the device
• Conservation of electric currents
• Radiation through the ambient environment

In order to analyze such phenomena, the team used multiphysics modeling to bidirectionally couple heat transfer with electric currents, solving the two elements simultaneously. Solving this coupled electrical and thermal problem involved using a segregated solver approach, using an iterative linear system solver for the current substep and a direct solver for the thermal substep.

As for radiation, testing realistic sunlight conditions was possible via a solar source position functionality available in the Heat Transfer Module. The researchers further applied a uniform normal heating term of 100 W/m² as a smoothed ramp function that ramps from 0 to 100 W/m² over 0.1 s. This is illustrated in the plot below. The model featured a fixed operating temperature of 25 K at the bottom boundary, with a convective heat flux applied to all other boundaries in order to simulate the small cooling effect caused by cooled air inside the bolometer.

A plot showing radiation heating as a function of time. Image by J. Thomas, J.S. Crompton, and K.C. Koppenhoefer and taken from their COMSOL Conference presentation.

Analyzing Bolometer Sensitivity

Now, let’s turn our attention to the sensitivity study. While there are multiple factors affecting the sensitivity of a bolometer — strip spacing, strip aspect ratio, materials, and operating temperatures — the focus here was evaluating the impact of specific design parameters.

In their study, the researchers chose to model a copper material absorbing strip with temperature-dependent material properties. Why copper? As an absorbent material with a strong dependence of conductivity to temperature, copper enabled the team to achieve the greatest sensitivity in their chosen temperature range, 10-50 K (cryogenic temperatures).

Graph showing the electrical conductivity as a function of T. Here, we can see the most sensitive temperature range for a copper material. Image by J. Thomas, J.S. Crompton, and K.C. Koppenhoefer and taken from their COMSOL Conference paper submission.

One point of interest was the dimensions of the contact strip. For this analysis, the team utilized the loft feature in the Design Module for automatic parameterization of the strip spacing parameter. They also generated a free tetrahedral mesh using the default physics-controlled mesh in COMSOL Multiphysics.

Left: Parameterization of the strip spacing. Right: Tetrahedral mesh. Images by J. Thomas, J.S. Crompton, and K.C. Koppenhoefer and taken from their COMSOL Conference paper submission.

The simulation analyses generated results for the temperature, current flow, and voltage caused by incident radiation at 0.2 s. Sensitivity, represented by S in this study, was defined as the change in voltage divided by the amount of absorbed incident light wattage.

Temperature (left), current flow (middle), and change in voltage caused by incident radiation (right) at 0.2 s. Images by J. Thomas, J.S. Crompton, and K.C. Koppenhoefer and taken from their COMSOL Conference paper submission.

To judge how strip spacing affects sensitivity, the researchers performed a parametric sweep for different strip spacing values. In order to account for the voltage drop change for the different configurations of the serpentine length, the sensitivity was normalized by an initial voltage drop. As the graph below indicates, increasing the space between the mounting board and serpentine absorber led to improved bolometer sensitivity. These results provided valuable information to the team at AltaSim, allowing them to move forward in creating a sensitive bolometer design that can more accurately detect and measure the power of incident electromagnetic radiation.

A graph highlighting the effects of strip spacing on bolometer sensitivity. Image by J. Thomas, J.S. Crompton, and K.C. Koppenhoefer and taken from their COMSOL Conference paper submission.

Simulation Helps to Advance Bolometer Research and Design

The simulation study presented here can be used to create customized bolometer designs for specific applications and identify other methods for maximizing device sensitivity. For the research team at AltaSim, the computational model can further serve as a foundation for examining additional design parameters that affect the sensitivity of the device. For example, they could study materials that are specially designed to be sensitive to conductivity at room temperatures. Further points of focus in the team’s simulation research include analyzing the serpentine geometry, strip material selection, and bias current magnitude.

Learn More About AltaSim’s Uses of Multiphysics Simulation

• Take a look at the full paper: “Multiphysics Analysis of an Infrared Bolometer“
• Read this blog post to learn about how AltaSim is designing and deploying simulation apps for a variety of uses