# Structural Mechanics

Solve linear static, transient, modal analysis, and frequency response problems

With structural analysis, you can predict how components behave under loading, vibration, and other physical effects. This helps you design robust mechanical components by validating designs through simulation and reducing the need for physical testing.

The toolbox lets you perform linear static analysis, transient analysis, modal analysis, and frequency response analysis. A typical programmatic workflow for solving a structural problem includes these steps:

• Create a special structural analysis container for a solid (3-D), plane stress, or plane strain model.

• Define 2-D or 3-D geometry and mesh it.

• Assign structural properties of the material, such as Young's modulus, Poisson's ratio, and mass density.

• Specify a damping model and its values for a dynamic problem.

• Specify gravitational acceleration as a body load.

• Specify boundary loads and constraints.

• Specify initial displacement and velocity for a dynamic problem.

• Solve the problem and plot results, such as displacement, velocity, acceleration, stress, strain, von Mises stress, principal stress and strain.

• Approximate dynamic characteristics of a structural model by using reduced order modeling (ROM).

## Functions

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 `createpde` Create model `structuralProperties` Assign structural properties of material for structural model `structuralDamping` Specify damping parameters for transient or frequency response structural model `structuralBodyLoad` Specify body load for structural model `structuralBoundaryLoad` Specify boundary loads for structural model `structuralBC` Specify boundary conditions for structural model `structuralIC` Set initial conditions for a transient structural model `structuralSEInterface` Specify structural superelement interface for component mode synthesis `solve` Solve heat transfer, structural analysis, or electromagnetic analysis problem `assembleFEMatrices` Assemble finite element matrices `reduce` Reduce structural model `reconstructSolution` Recover full-model transient solution from reduced-order model results `linearize` Linearize structural or thermal model `linearizeInput` Specify inputs to linearized model `linearizeOutput` Specify outputs of linearized model
 `evaluateStress` Evaluate stress for dynamic structural analysis problem `evaluateStrain` Evaluate strain for dynamic structural analysis problem `evaluateVonMisesStress` Evaluate von Mises stress for dynamic structural analysis problem `evaluateReaction` Evaluate reaction forces on boundary `evaluatePrincipalStress` Evaluate principal stress at nodal locations `evaluatePrincipalStrain` Evaluate principal strain at nodal locations
 `interpolateDisplacement` Interpolate displacement at arbitrary spatial locations `interpolateVelocity` Interpolate velocity at arbitrary spatial locations for all time or frequency steps for dynamic structural model `interpolateAcceleration` Interpolate acceleration at arbitrary spatial locations for all time or frequency steps for dynamic structural model `interpolateStress` Interpolate stress at arbitrary spatial locations `interpolateStrain` Interpolate strain at arbitrary spatial locations `interpolateVonMisesStress` Interpolate von Mises stress at arbitrary spatial locations
 `pdeplot` Plot solution or mesh for 2-D problem `pdeplot3D` Plot solution or surface mesh for 3-D problem `pdegplot` Plot PDE geometry `pdemesh` Plot PDE mesh `pdeviz` Create and plot PDE visualization object
 `findStructuralProperties` Find structural material properties assigned to geometric region `findStructuralDamping` Find damping model assigned to structural dynamics model `findStructuralBC` Find structural boundary conditions and boundary loads assigned to geometric region `findStructuralIC` Find initial displacement and velocity assigned to geometric region `findBodyLoad` Find body load assigned to geometric region

## Objects

 `StructuralModel` Structural model object `ReducedStructuralModel` Reduced order structural model results `StaticStructuralResults` Static structural solution and its derived quantities `TransientStructuralResults` Transient structural solution and its derived quantities `ModalStructuralResults` Structural modal analysis solution `FrequencyStructuralResults` Frequency response structural solution and its derived quantities

## Properties

 StructuralMaterialAssignment Properties Structural material property assignments StructuralDampingAssignment Properties Damping assignment for a structural analysis model StructuralSEIAssignment Properties Superelement interface assignment for structural model BodyLoadAssignment Properties Body load assignments StructuralBC Properties Boundary condition or boundary load for structural analysis model GeometricStructuralICs Properties Initial displacement and velocity over a region NodalStructuralICs Properties Initial displacement and velocity at mesh nodes PDESolverOptions Properties Algorithm options for solvers PDEVisualization Properties PDE visualization of mesh and nodal results

## Topics

### Structural Analysis Workflow

Deflection Analysis of Bracket

Analyze a 3-D mechanical part under an applied load and determine the maximal deflection.

Stress Concentration in Plate with Circular Hole

Perform a 2-D plane-stress elasticity analysis.

Structural Dynamics of Tuning Fork

Perform modal and transient analysis of a tuning fork.

Dynamics of Damped Cantilever Beam

Include damping in the transient analysis of a simple cantilever beam.

Modal Superposition Method for Structural Dynamics Problem

Use modal analysis results to compute the transient response of a thin 3-D plate under a harmonic load at the center.

Thermal Deflection of Bimetallic Beam

Solve a coupled thermo-elasticity problem.

Axisymmetric Thermal and Structural Analysis of Disc Brake

Simplify analysis of a disc brake by using an axisymmetric model for thermal and thermal stress computations.

Vibration of Square Plate

Calculate the vibration modes and frequencies of a 3-D simply supported, square, elastic plate.

Reduced-Order Modeling Technique for Beam with Point Load

Eliminate degrees of freedom that are not on the boundaries of interest by using the Craig-Bampton ROM technique.

Modal and Frequency Response Analysis for Single Part of Kinova® Gen3 Robotic Arm

Analyze shoulder link of Kinova® Gen3 Ultra lightweight robot arm for deformations under applied pressure.

Thermal Stress Analysis of Jet Engine Turbine Blade

Compute the thermal stress and deformation of a turbine blade in its steady-state operating condition.

### General PDE Workflow

Deflection of Piezoelectric Actuator

Solve a coupled elasticity-electrostatics problem.

Clamped Square Isotropic Plate with Uniform Pressure Load

Calculate the deflection of a structural plate acted on by a pressure loading.

Dynamic Analysis of Clamped Beam

Analyze the dynamic behavior of a beam clamped at both ends and loaded with a uniform pressure load.

Vibration of Circular Membrane

Find vibration modes of a circular membrane.

Finite Element Analysis of Electrostatically Actuated MEMS Device

Perform coupled electro-mechanical finite element analysis of an electrostatically actuated micro-electro-mechanical (MEMS) device.

### Structural Mechanics Equations

Linear Elasticity Equations

Linear elasticity equations for plane stress, plane strain, and 3-D problems.

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