Unified Modeling

Solve structural mechanics, heat transfer, and electromagnetic problems with a unified workflow using a finite element analysis model

The unified finite element model workflow lets you solve structural, thermal, and electromagnetic problems and switch between the types of problems. This workflow uses an femodel object and its properties to define the type of problem and all its parameters. This model enables you to specify physical parameters for all three types of analyses, and uses the parameters appropriate for the current analysis type.

A typical unified modeling workflow includes these steps:

Create an femodel container while specifying the analysis type and the geometry for a model.
Mesh the geometry.
Specify physical parameters of the problem using familiar domain-specific terms.
Solve the problem to obtain results at nodal locations.
Optionally, interpolate results at arbitrary spatial locations.
Visualize results by using the Visualize PDE Results Live Editor task or the plotting functions available in Partial Differential Equation Toolbox™.
Switch the analysis type as needed to solve the new problem.

Functions

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Problem Setup

`generateMesh`	Create triangular or tetrahedral mesh
`solve`	Solve structural analysis, heat transfer, or electromagnetic analysis problem
`triangulation`	Create `triangulation` object from `fegeometry` (Since R2023b)
`setupRadiation`	Specify radiation parameters for surface-to-surface heat transfer (Since R2023b)
`assembleFEMatrices`	Assemble finite element matrices
`reduce`	Reduce structural or thermal model (Since R2019b)

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)

Postprocessing for Structural Mechanics

`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
`filterByIndex`	Access transient results for specified time steps (Since R2023b)
`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

Postprocessing for Heat Transfer

`interpolateTemperature`	Interpolate temperature in thermal result at arbitrary spatial locations
`evaluateTemperatureGradient`	Evaluate temperature gradient of thermal solution at arbitrary spatial locations
`evaluateHeatFlux`	Evaluate heat flux of thermal solution at nodal or arbitrary spatial locations
`evaluateHeatRate`	Evaluate integrated heat flow rate normal to specified boundary
`filterByIndex`	Access transient results for specified time steps (Since R2023b)

Postprocessing for Electromagnetics

`generateMaxwellStressTensor`	Compute Maxwell stress tensor at nodal locations (Since R2024a)
`interpolateMaxwellStressTensor`	Interpolate Maxwell stress tensor at arbitrary spatial locations (Since R2024a)
`interpolateElectricPotential`	Interpolate electric potential in electrostatic or DC conduction result at arbitrary spatial locations (Since R2021a)
`interpolateElectricField`	Interpolate electric field in electrostatic or DC conduction result at arbitrary spatial locations (Since R2021a)
`interpolateElectricFlux`	Interpolate electric flux density in electrostatic result at arbitrary spatial locations (Since R2021a)
`interpolateMagneticPotential`	Interpolate magnetic potential in magnetostatic result at arbitrary spatial locations (Since R2021a)
`interpolateMagneticField`	Interpolate magnetic field in magnetostatic result at arbitrary spatial locations (Since R2021a)
`interpolateMagneticFlux`	Interpolate magnetic flux density in magnetostatic result at arbitrary spatial locations (Since R2021a)
`interpolateHarmonicField`	Interpolate electric or magnetic field in harmonic result at arbitrary spatial locations (Since R2022a)
`interpolateCurrentDensity`	Interpolate current density in DC conduction result at arbitrary spatial locations (Since R2022b)

Live Editor Tasks

Visualize PDE Results

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

Objects

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Model, Geometry, and Materials

`femodel`	Finite element analysis model object (Since R2023a)
`fegeometry`	Geometry object for finite element analysis (Since R2023a)
`materialProperties`	Material properties for structural, thermal, and electromagnetic analysis (Since R2023a)

Boundary Conditions

`edgeBC`	Boundary conditions on geometry edge (Since R2023a)
`faceBC`	Boundary conditions on geometry face (Since R2023a)
`vertexBC`	Boundary conditions on geometry vertex (Since R2023a)
`farFieldBC`	Absorbing boundary condition for harmonic electromagnetic analysis (Since R2023a)

Loads

`cellLoad`	Load on geometry cell (Since R2023a)
`faceLoad`	Load on geometry face (Since R2023a)
`edgeLoad`	Load on geometry edge (Since R2023a)
`vertexLoad`	Load on geometry vertex (Since R2023a)
`surfaceToSurfaceSettings`	Settings for modeling thermal radiation between surfaces (Since R2023b)

Initial Conditions and Initial Guesses

`cellIC`	Initial conditions on geometry cell (Since R2023a)
`faceIC`	Initial conditions on geometry face (Since R2023a)
`edgeIC`	Initial conditions on geometry edge (Since R2023a)
`vertexIC`	Initial conditions on geometry vertex (Since R2023a)

Results

`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)
`SteadyStateThermalResults`	Steady-state thermal solution and derived quantities
`TransientThermalResults`	Transient thermal solution and derived quantities
`ModalThermalResults`	Modal thermal solution (Since R2022a)
`ElectrostaticResults`	Electrostatic solution and derived quantities (Since R2021a)
`MagnetostaticResults`	Magnetostatic solution and derived quantities (Since R2021a)
`HarmonicResults`	Harmonic electromagnetic solution (Since R2022a)
`ConductionResults`	DC conduction solution (Since R2022b)

Reduced Models

`romInterface`	Reduced-order model (ROM) interface (Since R2024a)
`ReducedStructuralModel`	Reduced-order structural model results (Since R2019b)
`ReducedThermalModel`	Reduced-order thermal model (Since R2022a)

Properties

PDESolverOptions Properties	Algorithm options for solvers
PDEVisualization Properties	PDE visualization of mesh and nodal results (Since R2021a)

Topics

Unified Workflow Basics

Migration from Domain-Specific to Unified Workflow
Migrate existing code for structural, thermal, and electromagnetic problems to a unified workflow.
Nonconstant Parameters of Finite Element Model
Specify nonconstant parameters of a finite element model by using a function handle.
Rectangular, Triangular, Trapezoidal, and Harmonic Loads
Use helper functions to model harmonic and step loads for a finite element model.

Structural Mechanics

Deflection Analysis of Bracket
Analyze a bracket under an applied load and determine the maximal deflection by using the unified workflow.
Structural Dynamics of Tuning Fork
Perform modal and transient analysis of a tuning fork.
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.
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.

Heat Transfer

Heat Transfer in Block with Cavity
Find the heat distribution in a block with a cavity by using the unified workflow.
Temperature Distribution in Heat Sink
Perform a 3-D transient heat transfer analysis of a heat sink.
Heat Distribution in Circular Cylindrical Rod
Analyze a 3-D axisymmetric model by using a 2-D model.
Heat Conduction in Multidomain Geometry with Nonuniform Heat Flux
Perform a 3-D transient heat conduction analysis of a hollow sphere made of three different layers of material, subject to a nonuniform external heat flux.
Inhomogeneous Heat Equation on Square Domain
Solve the heat equation with a source term.
Heat Transfer Problem with Temperature-Dependent Properties
Solve the heat equation with a temperature-dependent thermal conductivity.
Heat Transfer in Orthotropic Material Plate due to Laser Beam
Compute temperature distribution on a square plate made of orthotropic material with a heat flux generated by a laser beam.
Radiation Heat Transfer in Spherical Cavity
This example shows the effect of surface-to-surface radiation in thermal analysis of nested annular spheres.

Electromagnetics

Electrostatic Potential in Air-Filled Frame
Find the electrostatic potential in an air-filled annular quadrilateral frame by using the unified workflow.
Electrostatic Analysis of Transformer Bushing Insulator
Compute an electric field intensity in a bushing insulator.
Magnetic Flux Density in Electromagnet
Compute a magnetic flux density in a solenoid with an iron core using a 3-D model and a 2-D axisymmetric model.
Magnetic Flux Density in H-Shaped Magnet
Compute a magnetic flux density in a ferromagnetic frame.
Magnetic Flux Density in H-Shaped Magnet with Nonlinear Relative Permeability
Solve a 2-D nonlinear magnetostatic problem of a ferromagnetic frame with an H-shaped cavity by using the unified workflow.
Current Density Between Two Metallic Conductors
Find the electric potential and the components of the current density between two circular metallic conductors.
Magnetic Field in Two-Pole Electric Motor
Find the static magnetic field induced by the stator windings in a two-pole electric motor.
Scattering Problem
Compute reflected waves from an object illuminated by incident waves.

Featured Examples

Thermal and Structural Analysis of Disc Brake

Compute temperature distribution and thermal stress on a disc brake by using the unified workflow.

Open Live Script

Effect of Surface-to-Surface Radiation on Battery Module Under Thermal Runaway Condition

Include surface-to-surface radiation effects in thermal analysis of a battery module. The example analyzes a 18650 Li-ion battery module consisting of nine cells, connectors at both ends, and the casing. The space between the cells and the casing is free space, and any conductive heat transfer due to stagnant air is ignored. The example accounts for heat exchange due to conduction through material and radiation between surfaces. The conduction heat transfer path consists of components in thermal contact. Radiated heat exchange between components not in thermal contact becomes significant at higher temperatures, such as in thermal runaway conditions. The example simulates a thermal runaway scenario by imposing a large heat generation load on one of the cells in the module.

Open Live Script

Uniformly Charged Sphere: Force Exerted by Southern Hemisphere on Northern Hemisphere

Find the force that the southern hemisphere of the uniformly charged sphere exerts on its northern hemisphere.

Open Live Script