## Structural Mechanics Module Updates

For users of the Structural Mechanics Module, COMSOL Multiphysics^{®} version 5.3a brings bolt thread contact modeling, a more general fluid-structure interaction multiphysics coupling, and improved default plots for better visualizations. Learn about these structural mechanics features and more below

### Bolt Thread Contact Modeling

When modeling bolted connections, the stress state in the vicinity of the bolt hole can be significantly influenced by the wedging effect caused by the contact pressure between the internal and external thread. However, it is seldom possible to include the actual geometry of the threads due to model size and meshing considerations. The new *Bolt Thread Contact* feature in the *Solid Mechanics* interface makes it possible to model the two threaded parts while using only cylindrical surfaces in the geometry. With this feature, you are able to incorporate the salient effects of the threaded connection.

Comparison of stress normal to a cut plane through the bolts. The bolt to the right is modeled using the new bolt thread contact condition, whereas the bolt to the left is joined to the bolt hole using a continuity condition. Note the example of the settings in the *Bolt Thread Contact* node.

*Bolt Thread Contact*node.

### Improvements for Bolt Pre-Tension

The *Bolt Pre-Tension* feature can now be added in 2D axisymmetric components for the *Solid Mechanics* interface. By necessity, the bolt is located at the axis of revolution for 2D axisymmetric cases. Additionally, in the *Bolt Selection* subnode, in both 3D and 2D axisymmetry, you can now specify a relaxation of the bolt predeformation, which can be a function of time and loading history, for example.

### New Fluid-Structure Interaction Interface

A new *Fluid-Structure Interaction* multiphysics coupling has replaced the interface used in previous versions of the COMSOL^{®} software. The new coupling matches the modern style, with a number of single-physics interfaces and multiphysics nodes to couple them together. With this approach, all functionality in the constituent physics interfaces is available for fluid-structure interaction (FSI) modeling. On the structural side, many additional boundary conditions and material models are now available for FSI analysis; for example, rigid domain, piezoelectric, and nonlinear elastic material models. On the fluid side, all turbulence models are now available as well as a number of new boundary conditions.

Additionally, you have more flexibility when building and solving a model. You can start with a single-physics model, either structural mechanics or fluid flow, before adding the fluid-structure interaction, and you can disable a physics interface in an already coupled model to solve for only one physics. The new functionality facilitates adding a third physics, such as heat transfer, and even additional physics beyond that. Finally, the moving mesh, now its own node under *Definitions*, can be disabled and enabled as needed.

After adding a *Fluid-Structure Interaction* interface from the Model Wizard, you will get a *Solid Mechanics* interface, a *Laminar Flow* interface, a *Fluid-Structure Interaction* multiphysics coupling node, and a *Moving Mesh* node in the *Definitions* section. All fluid-structure interaction models in the Application Libraries have been updated to include this new coupling functionality.

The peristaltic pump model has been updated to include the new *Fluid-Structure Interaction* interface coupling.

*Fluid-Structure Interaction*interface coupling.

### Generalized Plane Strain

For 2D solid mechanics, a generalized plane strain formulation has been developed as a third option to the plane strain and plane stress approximations. The generalized plane strain approximation is intended for modeling the central part of structures that are long and have a constant cross section. For these cases, as opposed to a standard plane strain formulation, nonzero out-of-plane strains are present.

When selecting the type of 2D approximation, you can choose the *Generalized plane strain* formulation.

*Generalized plane strain*formulation.

### Coupling Beams and Solids

The *Solid-Beam Connection* multiphysics coupling, in 2D, includes one more type of connection: *Solid and beam shared boundaries*. Additionally, the coupling is now available in 3D, and three fundamentally different types of connections can be modeled:

1. A point of a beam is connected to a boundary, or part of a boundary, on the solid. The connected region is rigidly coupled to the point on the beam.

2. An edge with a beam representation is connected to a boundary on the solid. All nodes on the solid that are within a certain transverse distance from the beam are connected.

3. A transition from a beam to a solid is modeled. In this case, the solid is assumed to be a 3D representation of the beam cross section, and beam theory assumptions are used when formulating the connection. Even the warping of the cross section is taken into account.

The *Solid-Beam Connection* coupling is used for modeling the transition from a solid to a beam. The load is visualized using the new Point Arrow plot type.

*Solid-Beam Connection*coupling is used for modeling the transition from a solid to a beam. The load is visualized using the new Point Arrow plot type.

### Improved Default Plots

The default plots in the structural mechanics physics interfaces have been updated to produce more informative visualizations. The Application Library tutorials have been updated accordingly. Some of the more prominent changes that you will see are as follows:

- The color table for von Mises stress plots is RainbowLight
- The color table for mode shape plots, for eigenfrequency and linear buckling studies, is AuroraBorealis
- Mode shape plots have the legend switched off to emphasize that the amplitude of a mode does not have a physical meaning
- The color table for section force plots in the
*Beam*and*Truss*interfaces is Wave, with a symmetric color range- This makes it possible to immediately distinguish between tension and compression, for example

- In contact analysis, a plot of the contact pressure is added, as either a line plot (2D) or contour plot (3D)
- The default plot for Stress Linearization now has a legend for the graphs
- The default Undeformed geometry plot, produced by the
*Shell*interface, has new colors - When a material model like plasticity or creep is used, a contour plot of a relevant strain quantity, like the effective plastic strain, overlays the stress plot
- Applicable for the Nonlinear Structural Materials Module and the Geomechanics Module

- In the
*Fatigue*interface, the Traffic color table is used for predicted cycles to failure and for usage factors- Applicable for the Fatigue Module

*In this example, you can see brighter colors in the stress plot (RainbowLight color table), and plastic strain contours and contact pressure contours have been added by default. For comparison, a plot from the default plot in COMSOL Multiphysics*

^{®}version 5.3 of the same model is shown.^{®}version 5.3 of the same model is shown.

### Improved Plots for Principal Values

The plot type Principal Stress can now be used for any kind of tensor principal values. In earlier versions of the COMSOL^{®} software, only a single predefined stress or strain field could be selected, but now you can manually enter orientation vectors and corresponding principal values.

A new set of principal strains have been added to the results in the *Solid Mechanics* interface: Principal logarithmic strains. This is the logarithmic strain, or "true" strain, with orientations given in a space-fixed coordinate system, well suited for plotting on the deformed geometry in a geometrically nonlinear analysis.

Also, a new Principal Stress Line plot type has been added that is particularly useful in the *Shell* and *Plate* interfaces. Previously, the principal value plots were only available for volumes and surfaces.

*Logarithmic strains plotted on a deformed rubber seal.*

### C and Hat Cross Sections in the Beam Interface

Two more built-in cross section types have been added to the *Beam* interface: C-profile and Hat.

### Detailed Control Over Constraints

All constraints in the structural mechanics interfaces have been augmented with an option to exclude the constraints on lower geometric entity levels. As an example, a *Prescribed Displacement* on a boundary can now be disabled on the boundary's edges or points. This is useful when you need to fine-tune your constraints, such as when there are duplicates or conflicts between constraints.

### Eigenfrequency Analysis of Contact Problems

You can now compute eigenfrequencies following an analysis that includes a contact problem, for example, to study the influence that the preload in a bolted structure has on its eigenfrequencies.

### Mechanical Losses Associated to Thermal Stress

The *Thermal Expansion* multiphysics coupling node now automatically handles the mechanical losses due to thermal stress; the generated heat source is added to the heat transfer equation in the corresponding domains. A *Mechanical losses* check box is available in the new *Heat Sources* section of the *Thermal Expansion* node to control this behavior.

### Additions to Safety Factor Computations

The *Safety* feature has been augmented in two respects. First, in the *Membrane* interface, the Modified Tsai-Hill, Norris, Azzi-Tsai-Hill, Hoffman, Tsai-Wu orthotropic, and Tsai-Wu criteria have all been added. Second, failure criteria for concrete (Bresler-Pister, Willam-Warnke, and Ottosen) have been added for the *Solid Mechanics*, *Shell*, *Plate*, and *Beam Cross Section* interfaces.

### New Fluid-Structure Interaction Interface That Supports All Turbulence Models

A new *Fluid-Structure Interaction* multiphysics coupling has replaced the interface used in previous versions of the COMSOL^{®} software. The new coupling matches the modern style, with a number of single-physics interfaces and multiphysics nodes to couple them together. With this approach, all functionality in the constituent physics interfaces is available for fluid-structure interaction (FSI) modeling. On the structural side, many additional boundary conditions and material models are now available for FSI analysis; for example, rigid domain, piezoelectric, and nonlinear elastic material models. On the fluid side, all turbulence models are now available as well as a number of new boundary conditions. After adding a *Fluid-Structure Interaction* interface from the Model Wizard, you will get a *Solid Mechanics* interface, a *Laminar Flow* interface, a *Fluid-Structure Interaction* multiphysics coupling node, and a *Moving Mesh* node in the *Definitions* section. All fluid-structure interaction models in the Application Libraries have been updated to include this new coupling functionality.

*Pressure (color table) and deformation (exaggerated by a factor of 50 at the surface) of a sports car wing subjected to turbulent flow (streamlines) of 200 km/h (125 mph) in a test bench. The model is defined using one-way fluid-structure interaction in the new physics interface.*

### Updated Tutorial Model: Lumped Loudspeaker Driver Using Lumped Mechanical System

This is a model of a moving-coil loudspeaker where a lumped parameter analogy represents the behavior of the electrical and mechanical speaker components. The Thiele-Small parameters (small-signal parameters) serve as input to the lumped model. In this model, the mechanical speaker components such as moving mass, suspension compliance, and suspension mechanical losses are modeled using the *Lumped Mechanical System* interface.

*Pressure field plotted as isosurfaces (above the speaker cone) and as a surface plot (below the speaker cone).*

**Application Library path:**

*Acoustics_Module/Electroacoustic_Transducers/lumped_loudspeaker_driver_mechanical*

### New Tutorial Model: Vibroacoustic Loudspeaker Simulation, Multiphysics with BEM-FEM

This model shows a full vibroacoustic analysis of a loudspeaker including the driver, cabinet, and stand. It applies a nominal driving voltage to extract the resulting sound pressure level in the cabinet and in the outside room, as well as the deformation of the cabinet and driver, for a given frequency. The loudspeaker is located on a hard floor some distance from a wall located behind it. The example uses a hybrid BEM-FEM approach and couples the *Solid Mechanics, Shell*; *Pressure Acoustics, Frequency Domain*; and *Pressure Acoustics, Boundary Elements* physics interfaces. The model uses six built-in multiphysics couplings to connect the single-physics interfaces together.

Sound pressure level of the radiated acoustic field from a loudspeaker modeled using a full vibroacoustics simulation. The exterior acoustics are modeled using the new *Pressure Acoustics, Boundary Elements* interface, which is coupled to the FEM interfaces.

*Pressure Acoustics, Boundary Elements*interface, which is coupled to the FEM interfaces.

**Application Gallery link for example using the Pressure Acoustic, Boundary Elements interface:**

Vibroacoustic Loudspeaker Simulation: Multiphysics with BEM-FEM

### New Tutorial Model: Vibrating MEMS Micromirror with Viscous and Thermal Damping, Transient Behavior

Micromirrors are used in certain MEMS devices to control optical components. This example model, a vibrating micromirror surrounded by air, illustrates a mirror that is initially actuated for a short time and then exhibits damped vibrations. It uses the *Thermoviscous Acoustics, Transient*; the *Shell*; and the *Pressure Acoustics, Transient* interfaces to model the fluid-solid interaction in the time domain. Use of the *Thermoviscous Acoustics* interface provides full details of viscous and thermal damping of the mirror in relation to the surrounding air.

*Micromirror displacement and pressure distribution at a given time depicted in colors. The transient evolution of displacement of the mirror is depicted in the graph, showing the damped vibrations due to thermal and viscous losses.*

**Application Gallery link:**

Vibrating Micromirror with Viscous and Thermal Damping: Transient Behavior