### Opera-3d Stress Analysis Module

Opera-3d is a finite element (FE) software suite with capabilities for electromagnetic (EM), thermal and structural simulation. The suite includes a range of solver modules, including the 3d Stress Analysis Module which can calculate either displacements, strains and stresses due to external forces, or eigenmodes and natural frequencies of an unloaded structure.

### 3d Stress Analysis Module

The Stress Analysis module comprises two types of analysis: static stress, or eigenvalue. Static Stress (STRESS/ST) calculates the deformation, stresses and strains of a body subject to external and internal forces. Users can input the forces calculated from electromagnetic fields to the stress analysis. The simulation assumes small deformation within the elastic limit. Users can also include thermal expansion / contraction. Modal Stress (STRESS/EV) calculates the natural modes, i.e. the eigenvalues and eigenvectors, of a body without any internal or external forces. Because the stress module uses volume finite elements, it can be used with the same models that are used for electromagnetics and/or thermal analysis. Users may deploy the Static Stress Module in stand-alone mode with the user defining the distribution of forces, or as a multi-physics simulation with other Opera-3d modules providing the force or temperature distribution. Users can input the deformation computed by the stress analysis to modify the geometry in subsequent thermal and electromagnetic simulations

### Material Properties

The Stress module has analysis capabilities for isotropic, orthotropic and fully anisotropic materials. It may use the following material properties: Young’s modulus Poisson’s ratio Shear modulus Elasticity matrix (fully anisotropic materials) Thermal expansion coefficients (Static only) General expansion integrals (Static only) Density The material properties can be specified as numeric values or as expressions. For examples, the thermal expansion coefficients could be functions of temperature or position

### External Forces and Constraints

In the Modal Stress solver, constraints can be applied in any/all chosen directions. No external forces can be applied to a modal stress solution. In the Static Stress Solver external forces and constraints can be applied globally or as boundary conditions on the surfaces of the model. The available constraints are:

• Fixed:
• in all 3 directions:
• in tangential directions:
• in the direction normal to the surface;
• Defined normal displacement;
• Defined displacement in all 3 directions;
• Thermal expansion, with values of reference and operating temperatures, which can be imported from thermal analysis, and
• General expansion, which can be used to model magnetostriction, electrostriction and piezo effects, with the expansion integrals expressed as functions of magnetic or electric field vectors imported from electromagnetic analysis.

The available surface forces are:

• pressure, a force normal to the surface and
• traction, a force in any direction.

Gravitational forces can be applied in the direction of one of the Cartesian coordinate axes.

### Modeller and Post Processor

Opera-3d provides a geometric modeller used for model data definition, and a geometric post-processor for results analysis. The Graphical User Interface (GUI) offers access to features specifically tailored for multi-physics design. Users can program regularly performed actions into parameterized macro-files. The Modeller allows users to create models, define material properties, set boundary conditions and loads, create the mesh and launch the calculations. Opera-3d meshing has facilities for creating hexahedral, prism and tetrahedral meshes (the mesh can be a mixture of types). Meshing is automatic, requiring little or no user setting in many cases. However, it does include facilities to finely control the mesh when required. Simulations are controlled by the Opera Manager, which also allows jobs to be submitted to remote machines and/or across a number of shared memory cores. Users can store solutions a database and interrogate them using the Opera Post Processor.

### Applications

• Motors
• Generators
• Charged particle devices
• Electromagnetic brakes
• Actuators
• Transducers
• Transformers
• Magnets
• Shields

### Tools

• Full 3d modelling
• Static Stress analysis
• Modal Stress analysis
• Isotropic and anisotropic materials
• User defined functions
• Coupling to EM and thermal analysis
• Extendible Post-Processing

### Post-processing

• Graphs & histograms of the solution
• Contours of the results on any surface
• Vector display of results quantities:
• Displacements
• Strains (Principal, Component, Invariants, Equivalent)
• Stress (Principal, Component, Invariants, Equivalent, Von Mises)
• Deformed Shape
• Eigenmodes
• Natural Frequencies
• Surface and volume integrals