## Structural Mechanics Module Updates

For users of the Structural Mechanics Module, COMSOL Multiphysics^{®} version 5.4 brings response spectrum analysis functionality, homogenization of material data using representative volume elements, and the activation of material. Browse these structural mechanics features and more below.

### Response Spectrum Analysis

There is new functionality for response spectrum analysis, which is used for estimating the peak response of short and nondeterministic dynamic events. There is support for several modal combination methods, such as SRSS, CQC (der Kiureghian), absolute sum, ten percent, grouping, and double sum (Rosenblueth). Four spatial combination methods are available: SRSS, 100-40-40, CQC3, and SRSS3. It is possible to separate periodic and rigid modes using the Gupta and Lindley-Yow methods, and to add a static correction for mass not represented by the eigenmodes. This functionality is available in the Model Wizard through a preset study type called *Response Spectrum*, which adds a number of features to the model tree for setting up the analysis.

There are two new models that utilize these features:

*Maximum displacements in a framework during an earthquake (left). Horizontal and vertical design response spectra (right).*

*Maximum displacements in a framework during an earthquake (left). Horizontal and vertical design response spectra (right).*

### Representative Volume Elements (RVE) for Homogenization of Periodic Materials

For many types of inhomogeneous materials, it is possible to compute effective material data by studying the smallest repetitive structure by using periodic boundary conditions. Such a cell is often called a representative volume element (RVE). The new *Cell Periodicity* feature automates the setup of boundary conditions and loads for such a cell, and you can compute anisotropic elasticity data and coefficients of thermal expansion for use in a macroscopic analysis. A new model, Micromechanical Model of a Composite, is available that demonstrates the functionality.

*The six fundamental deformation modes of a periodic cell representing a single fiber in a matrix, colored by effective stress.*

*The six fundamental deformation modes of a periodic cell representing a single fiber in a matrix, colored by effective stress.*

### Shell Interface for Axisymmetric Analysis

Axially symmetric shell structures are common in engineering. The *Shell* interface is now available for 2D axisymmetry, making the analysis of such structures more efficient. This is particularly important when studying multiphysics problems, such as acoustic-structure interaction.

See this feature demonstrated in the following models:

*The first eigenmode of a free cylindrical shell, shown as a revolved plot.*

*The first eigenmode of a free cylindrical shell, shown as a revolved plot.*

### New Fluid-Structure Interaction Couplings

The fluid-structure interaction (FSI) couplings have been extended to allow interaction with shells and membranes. At the same time, the *Fluid-Structure Interaction* multiphysics coupling has been redesigned so that the same coupling is used both for situations where the deformation of the fluid domain is important and when it can be ignored. There is also a new multiphysics coupling for fluid-structure interaction in assemblies, where the interface between structure and fluid does not have to be a common boundary with a shared mesh. This functionality is available in an extended version with the Multibody Dynamics Module for FSI that includes flexible and rigid bodies; see the Multibody Dynamics Module page for more details.

This feature is demonstrated in the following models:

*Flow through a ball check valve; streamlines colored by pressure.*

*Flow through a ball check valve; streamlines colored by pressure.*

### Activation of Material for Additive Manufacturing

In many manufacturing processes, material is added sequentially. In most cases, the material should be added in a stress-free state. With the new *Activation* feature, an *Attribute* for the *Linear Elastic Material* node, you can add and remove material based on a user-defined criterion. This criterion can be an arbitrary expression, which, for example, depends on time, parameter values, or temperature. You can see this functionality demonstrated in the Layered Plate model.

### Roller Condition with Analytical Normal Orientation

In the *Roller* boundary condition, you can now specify an analytical surface on which the structure slides. With this functionality, it is possible to also use the roller condition for finite displacements and rotations. The new functionality can be used to avoid situations where the normal vectors of a boundary surface may have less than perfect orientation, such as when using imported meshes.

*A roller condition, defined as a cylindrical surface, is used at the middle section of this bar. The bar can freely rotate around its axis as well as translate axially.*

*A roller condition, defined as a cylindrical surface, is used at the middle section of this bar. The bar can freely rotate around its axis as well as translate axially.*

### Reaction-Free Symmetry Conditions

The symmetry conditions, in the structural mechanics interfaces, have been extended to account for cases where the symmetry plane is allowed to translate in the direction of its normal, rather than being a fixed plane. The reaction-free symmetry conditions are mainly used in truncated structures that have no net reaction force. In addition to being fully free to translate, the symmetry plane can also have a given displacement or a given net reaction force. You can see this functionality demonstrated in the Surface Resistor model.

*In this slice through a circuit board, the rightmost cut is allowed to expand with temperature, while remaining a plane.*

*In this slice through a circuit board, the rightmost cut is allowed to expand with temperature, while remaining a plane.*

### New Study Types for Modal Superposition

Two new predefined study sequences for modal superposition have been added: *Time Dependent, Prestressed, Modal* and *Frequency Domain, Prestressed, Modal*. In both cases, three study steps are generated. The first one is a stationary step in which the prestress state used for the subsequent eigenfrequency computation is determined. Using these studies, it will be significantly easier to analyze prestressed structures with efficient modal superposition methods. Accordingly, some of the previous study types for dynamic analysis were renamed.

*Displacement amplitude and phase as function of loading frequency, with and without prestress.*

*Displacement amplitude and phase as function of loading frequency, with and without prestress.*

### Burgers Viscoelastic Model

The Burgers model has been added to the list of viscoelasticity material models. This is a constitutive model with similarities to a fluid in the sense that it is not long-time stable when subjected to a stress. The Burgers model can, for example, be used for modeling soils and biological materials.

*Schematic of the Burgers model for viscoelasticity.*

*Schematic of the Burgers model for viscoelasticity.*

### Rigid Connector for Edges and Points

Using rigid connectors is an important method when modeling mechanical assemblies. The selection in a *Rigid Connector* can now be a combination of boundaries, edges, and points. It is also possible to add a rigid connector directly at the edge and point levels. Connecting points is useful at bolted and riveted connections, for example.

### Flexible Formulation of the Rigid Connector Feature

There are now two formulations of the *Rigid Connector* feature: *Rigid* and *Flexible*. In the default *Rigid* formulation, all of the selected boundaries, edges, and points behave as if they were connected by a common rigid body. In some cases, this gives an unwanted stiffening or unrealistic local stresses. You can then switch to a *Flexible* formulation, where the constraint is applied only in an averaged sense. The flexible formulation is only available for a rigid connector with a pure boundary selection, not when the selection contains either edges or points.

### Utility Functions for External Materials

When programming your own constitutive relations using the external materials functionality, certain code segments are used repeatedly. This includes various tensor operations, computation of principal values and orientations, and matrix inversion. A new library with more than 20 utility functions covers many such common operations and significantly shortens the time spent writing code for material models.

### New Tutorial Models

COMSOL Multiphysics^{®} version 5.4 brings several new tutorial models.

#### Earthquake Analysis of a Building

**Search in the Application Library:**

*building_response_spectrum*

#### Shock Response of a Motherboard

*Peak displacements relative to the bolt positions in a gaming console motherboard during a postulated 50 g 11 ms shock, computed using response spectrum analysis.*

**Search in the Application Library:**

*motherboard_shock_response*

#### Connecting Beams and Solids

*In this tutorial model, the connection between solids and beams is explored. The plot shows how the results at a transition from a beam to a solid differ depending on the selected coupling options.*

**Search in the Application Library:**

*beam_solid_connection*

#### Prestress of Main Bearing Cap Bolts

*Stress in a cut through the bolt plane. The stresses at the bolt to the right, where accurate bolt thread modeling has been used, highlight the importance of using this technique, rather than assuming continuity between bolt and thread.*

**Search in the Application Library:**

*main_bearing_cap*

#### Micromechanical Model of a Composite

*Representative unit cell for a fiber composite with a 20% fiber fraction. The model is used for determining an equivalent averaged anisotropic material.*

**Search in the Application Library:**

*micromechanical_model_of_a_composite*

#### Spherical Cap with Central Point Load

*Deformation and force around the snap-through point when a point load acts on the top of a spherical shell.*

**Search in the Application Library:**

*spherical_cap_with_central_point_load*