With simulation software like COMSOL Multiphysics, saving computational time and memory is always a goal. The most important part of any simulation is obtaining an accurate answer, but after that, we want simulations to be swift and efficient. The Rigid Connector feature is used almost exclusively for this purpose. A simple, yet highly effective, feature in COMSOL, the Rigid Connector can replace geometric entities that aren’t significantly affected by structural displacement. In an elastic structure, there are two types of bodies: flexible and rigid. The flexible bodies account for basically all the deformation, while the rigid bodies are not significantly affected, allowing them to be modeled as Rigid Connectors. The Rigid Connector still needs to be included as a geometric entity, and even meshed for postprocessing reasons, but the elements in the mesh do not partake in the simulation computations. The feature allows the conditions at one end of the connector to translate directly to the other end of the connector.

Check out this mini-tutorial to see how to use the Rigid Connector feature:

As is the case with the Rigid Connector feature, performing a linear buckling analysis can also be categorized as “simple, yet effective”. One difference though; linear buckling is actually a study type, unlike the Rigid Connector, which is a boundary condition. A linear buckling analysis estimates the *critical load* of a structure, that is, the maximum load the structure can withstand before failing. Knowing the maximum load a structure can bear allows you to adjust certain settings to protect the real-life structure from the same fate. COMSOL Multiphysics automatically runs a two-step process to return the critical buckling load solved during a linear buckling analysis. That’s done by performing a static analysis using a unit load, and by computing an eigenvalue problem associated with the static load. The first eigenvalue returned is associated with the critical buckling load.

Watch the video below for instructions on how to perform a linear buckling analysis:

*This is a supplementary video to the introductory structural mechanics video found on our YouTube channel.*

In this example, you will study the stress in a bracket connected to a pin where a load is applied. The pin is simulated as a rigid connector, saving computational time and memory. The bracket_basic model has been opened for this example.

Right click Model 1 and choose Add Physics. Select Structural Mechanics, Solid Mechanics, and click next. Select stationary as the study type and click Finish. Add the rigid connector that connects the holes in the bracket arms to simulate the presence of a pin. Under the Solid Mechanics node, select the Rigid Connector option. Choose Box 2 from the Selections list, and check the boxes for Prescribed in the X and Z directions. Apply a prescribed rotation of the rigid body around the y-axis, with a magnitude of one degree. Right-click Rigid Connector, choose Applied Force, and apply an external load of 100 Newtons in the negative y-direction. Under the solid mechanics node, choose More, Fixed constraint. Choose Box 1 from the selections list and right click Study 1 to compute the model.

The default plot shows the von Mises stress on a deformed geometry. You can see the effect that the pin’s rotation and applied force have on the bracket arms.

*For a more in depth look at this model, as well as similar models and videos, visit our website.*

*This is a supplementary video to the introductory structural mechanics video found on our YouTube channel.*

Linear buckling analysis provides an estimate of the critical load that can cause a sudden collapse of the structure. The bracket_basic model has been opened for this example.

Right-click Model 1 and choose add physics. Select Structural Mechanics>Solid Mechanics, and click next. Select linear buckling as the study type and choose Finish. Expand the Geometry node, and in the Import node click the browse button. Select the bracket symmetry model in the Structural Mechanics Module tutorial folder. Click Import and the geometry changes. We want the load direction to be 0 degrees and the peak load to be 1 Pascal. Right-click solid mechanics and choose More, Fixed constraint. Choose Box 1 from the Selection list. Apply a symmetry condition at the boundary in the symmetry plane. Select boundaries 43 and 44. Right-click solid mechanics and add a boundary load. Choose box two from the selections list and choose Rotated System 2 as the Coordinate system. Enter loadIntensity in the second row of the force table. Compute the study by right-clicking the Study 1 node.

The default plot shows the mode shape of the first buckling mode. Right-click Derived Values and choose Integration, Surface Integration. Locate the Selection section and choose Box 2. Type “lambda * load Intensity” into the expression section, multiplying the eigenvalue solved in the linear buckling analysis by the applied load, and evaluate it.

In the results table, you can see the Critical load factor is about 1.5e8, corresponding to a critical buckling load close to sixty thousand Newtons.

*For a more in depth look at this model, as well as similar models and videos, visit our website.*

In real-life situations the conditions are rarely perfect and certain measures need to be taken to account for varying circumstances. One of these unforeseen circumstances is a strain in the geometry, before an outside force is applied. For this example, an initial strain is added, simulating a reduction in pin length from 216 mm to 215 mm. The resulting von Mises stresses are calculated, and the initial strain in the x-direction can be seen.

Heat transfer is another circumstance that can affect a structural model. That is why the Structural Mechanics Module includes a *Thermal Stress* interface to model structural interactions resulting from heat transfer. The interface contains all the options that exist in the *Solid Mechanics* and *Heat Transfer* interfaces. In this video, the bracket arm holes are heated to 100 degrees Celsius, as if it was holding a structure at this temperature, and the resulting structural deformations are calculated and shown.

With both of these examples, the boundary load from the original static linear analysis is disregarded for simplicity. However, these two tutorials are paired together because they are not replacement models to the static linear analysis, but they can be *added* to the static linear analysis. You can start with a static linear analysis and then add either initial strain or thermal stress, or you could add both. We gave you the means, now it’s up to you to put all the pieces together.

Here’s a sneak peek at upcoming mini-tutorial videos in this series:

- Adding a Rigid Connector
- Adding Spring Conditions
- Modeling with the Shell Physics Interface
- Transient Analysis
- Eigenfrequency Analysis
- Prestressed Eigenfrequency Analysis
- Frequency Response Analysis
- Prestressed Frequency Response Analysis
- A Geometric Non-linear Problem: Linear Buckling Modeling
- Material Non-linearity: Elasto-plastic Material
- Modeling Contact Problems

We will continue to create structural mechanics videos over the next few weeks, but in the meantime you can find the complete model documentation for all of the analyses at www.comsol.com/bracket.

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In the above video, a bracket fixed in space by eight bolts is subjected to a load on its two arms. The load is given a magnitude and direction in which to exert its force on the bracket. The default solver shows the von Mises Stress distribution and an exaggerated deformation of the geometry. The postprocessing involves creating a volume integration to calculate the reaction forces. A parametric sweep is conducted, calculating the results for five different directions of the load. To help visualize the results, an exaggerated deformation is shown, with an arrow plot indicating the direction for each direction in the sweep. The reaction forces in the x, y, and z directions are calculated for each load angle and inserted into a 2D graph plot with ease. COMSOL’s core strength is the ability to compute multiple physics solutions at the same time. It also offers easy-to-use tools for displaying the results in an informative and aesthetically pleasing manner.

This an introduction example of the model, of which several additions are available including:

- Including Initial Strain
- Modeling Thermal Expansion
- Adding a Rigid Connector
- Adding Spring Conditions
- Modeling with the Shell Physics Interface
- Transient Analysis
- Eigenfrequency Analysis
- Prestressed Eigenfrequency Analysis
- Frequency Response Analysis
- Prestressed Frequency Response Analysis
- A Geometric Non-linear Problem: Linear Buckling Modeling
- Material Non-linearity: Elasto-plastic Material
- Modeling Contact Problems

Videos for these will be produced during the next few weeks, so keep you eye out for them on the blog or in our video center. You can, however, already find the complete model documentation for all of these analyses at www.comsol.com/bracket.

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