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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).

Functions

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Structural Model Setup

`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 (Since R2019b)
`solve`	Solve structural analysis, heat transfer, or electromagnetic analysis problem
`assembleFEMatrices`	Assemble finite element matrices
`reduce`	Reduce structural or thermal model (Since R2019b)
`reconstructSolution`	Recover full-model transient solution from reduced-order model (ROM) (Since R2019b)
`linearize`	Linearize structural or thermal model (Since R2021b)
`linearizeInput`	Specify inputs to linearized model (Since R2021b)
`linearizeOutput`	Specify outputs of linearized model (Since R2021b)

Solutions at Nodal Locations

`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

Solutions Interpolated to Custom 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

Visualization

`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 (Since R2021a)

Structural Model Properties

`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

Live Editor Tasks

Visualize PDE Results

Create and explore visualizations of PDE results in the Live Editor (Since R2022b)

Objects

`StructuralModel`	Structural model object
`ReducedStructuralModel`	Reduced-order structural model results (Since R2019b)
`StaticStructuralResults`	Static structural solution and derived quantities
`TransientStructuralResults`	Transient structural solution and derived quantities
`ModalStructuralResults`	Modal structural solution
`FrequencyStructuralResults`	Frequency response structural solution and derived quantities (Since R2019b)

Properties

StructuralMaterialAssignment Properties	Structural material property assignments
StructuralDampingAssignment Properties	Damping assignment for a structural analysis model
StructuralSEIAssignment Properties	Superelement interface assignment for structural model (Since R2019b)
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 (Since R2021a)

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.
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.
Linear Analysis of Cantilever Beam (Control System Toolbox)
Construct transient beam model and perform linear analysis.
Linear Analysis of Tuning Fork (Control System Toolbox)
Linearize a tuning fork structural model using Partial Differential Equation Toolbox™ software and perform linear analysis.

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.