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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).

von Mises stress plot in color


expand all

createpdeCreate model
structuralPropertiesAssign structural properties of material for structural model
structuralDampingSpecify damping parameters for transient or frequency response structural model
structuralBodyLoadSpecify body load for structural model
structuralBoundaryLoadSpecify boundary loads for structural model
structuralBC Specify boundary conditions for structural model
structuralICSet initial conditions for a transient structural model
structuralSEInterfaceSpecify structural superelement interface for component mode synthesis
solveSolve heat transfer, structural analysis, or electromagnetic analysis problem
assembleFEMatricesAssemble finite element matrices
reduceReduce structural model
reconstructSolutionRecover full-model transient solution from reduced-order model results
linearizeLinearize structural or thermal model
linearizeInputSpecify inputs to linearized model
linearizeOutputSpecify outputs of linearized model
evaluateStressEvaluate stress for dynamic structural analysis problem
evaluateStrainEvaluate strain for dynamic structural analysis problem
evaluateVonMisesStressEvaluate von Mises stress for dynamic structural analysis problem
evaluateReactionEvaluate reaction forces on boundary
evaluatePrincipalStressEvaluate principal stress at nodal locations
evaluatePrincipalStrainEvaluate principal strain at nodal locations
interpolateDisplacementInterpolate displacement at arbitrary spatial locations
interpolateVelocityInterpolate velocity at arbitrary spatial locations for all time or frequency steps for dynamic structural model
interpolateAccelerationInterpolate acceleration at arbitrary spatial locations for all time or frequency steps for dynamic structural model
interpolateStressInterpolate stress at arbitrary spatial locations
interpolateStrainInterpolate strain at arbitrary spatial locations
interpolateVonMisesStressInterpolate von Mises stress at arbitrary spatial locations
pdeplotPlot solution or mesh for 2-D problem
pdeplot3DPlot solution or surface mesh for 3-D problem
pdegplotPlot PDE geometry
pdemeshPlot PDE mesh
pdevizCreate and plot PDE visualization object
findStructuralPropertiesFind structural material properties assigned to geometric region
findStructuralDampingFind damping model assigned to structural dynamics model
findStructuralBCFind structural boundary conditions and boundary loads assigned to geometric region
findStructuralICFind initial displacement and velocity assigned to geometric region
findBodyLoadFind body load assigned to geometric region


StructuralModelStructural model object
ReducedStructuralModelReduced order structural model results
StaticStructuralResultsStatic structural solution and its derived quantities
TransientStructuralResultsTransient structural solution and its derived quantities
ModalStructuralResultsStructural modal analysis solution
FrequencyStructuralResultsFrequency response structural solution and its derived quantities


StructuralMaterialAssignment PropertiesStructural material property assignments
StructuralDampingAssignment PropertiesDamping assignment for a structural analysis model
StructuralSEIAssignment PropertiesSuperelement interface assignment for structural model
BodyLoadAssignment PropertiesBody load assignments
StructuralBC Properties Boundary condition or boundary load for structural analysis model
GeometricStructuralICs PropertiesInitial displacement and velocity over a region
NodalStructuralICs Properties Initial displacement and velocity at mesh nodes
PDESolverOptions PropertiesAlgorithm options for solvers
PDEVisualization PropertiesPDE visualization of mesh and nodal results


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.