Partial Differential Equation Toolbox
Solve Partial Differential Equations using Finite Element Method (FEM)
Partial Differential Equation Toolbox™ provides functions for solving structural mechanics, heat transfer, and general partial differential equations (PDEs) using finite element analysis.
You can perform linear static analysis to compute deformation, stress, and strain. For modeling structural dynamics and vibration, the toolbox provides a direct time integration solver. You can analyze a component’s structural characteristics by performing modal analysis to find natural frequencies and mode shapes. You can model conduction-dominant heat transfer problems to calculate temperature distributions, heat fluxes, and heat flow rates through surfaces. You can also solve standard problems such as diffusion, electrostatics, and magnetostatics, as well as custom PDEs.
Partial Differential Equation Toolbox lets you import 2D and 3D geometries from STL or mesh data. You can automatically generate meshes with triangular and tetrahedral elements. You can solve PDEs by using the finite element method, and postprocess results to explore and analyze them.
Get Started:
Linear Static Analysis
Compute displacement, stress, and strain under load and boundary conditions, and evaluate a component’s mechanical strength and behavior.
Deflection analysis of bracket.
Modal and Frequency Response Analysis
Find natural frequencies and mode shapes to identify and prevent potential resonances, and simulate dynamic behavior of a structure using its frequency responses.
First six mode shapes of a robotic arm.
Transient Analysis
Compute displacement, velocity, acceleration, stress, and strain under time-varying loads.
Deflection of a beam center as function of time.
Steady-State Thermal Analysis
Find temperature distributions and other thermal characteristics under constant thermal loads.
Thermal analysis of a multilayered pipe using FEA in MATLAB.
Transient Thermal Analysis
Find temperature distributions and other thermal characteristics under time-varying thermal loads.
Contour plots of temperature distribution with respect to time.
Coupled Thermal-Stress Analysis
Analyze mechanical behavior under coupled thermal and mechanical loads.
Stress distribution under combined mechanical and thermal loads.
Second-Order PDEs
Solve second-order linear and nonlinear PDEs for stationary, time-dependent, and eigenvalue problems.
L-shaped membrane with zero Dirichlet Boundary condition.
Electromagnetics
Solve electrostatics, magnetostatics, DC conduction, and wave propagation problems.
Electrostatic simulation of MEMS device.
Import/Create Geometry
Reconstruct 2D and 3D geometry from imported STL or mesh data, or create simple parameterized shapes using geometric primitives.
Import or create geometry in MATLAB.
Generate Mesh
Generate finite element mesh using triangular elements in 2D and tetrahedral elements in 3D. Inspect and analyze mesh quality to assess accuracy of results.
Generate mesh and ensure its quality for accuracy of results.
Plot and Animate Solutions
Visualize models and solutions by creating plots and animations of geometry, mesh, results, and derived and interpolated quantities by leveraging powerful MATLAB graphics. Create multiple subplots and easily customize plot properties.
Contour plot slices in 3D.
Postprocessing
Analyze solutions and its gradients at mesh nodes and other interpolated locations. Leverage MATLAB’s extensive functionalities for further statistical postprocessing and data analysis using Statistics and Machine Learning Toolbox and Optimization Toolbox.
Fast Fourier Transform of tip displacement.
FEA Workflows
Create a typical FEA workflow in MATLAB – import or create geometries, generate mesh, define physics with load, boundary, and initial conditions, solve, and visualize results – all from one user interface.
- Automate FEA simulations by using MATLAB® language, execute simulations faster leveraging Parallel Computing Toolbox™,
- integrate with other MATLAB products such as Simscape™ Multibody™ to build an end-to-end workflow,
- share custom applications using MATLAB Compiler™ and App Designer as a standalone application or as a web app.
MATLAB helps automate and integrate FEA workflows.
Axisymmetric Analysis
Speed up simulations by simplifying 3D solids of revolution by analyzing only the 2D axisymmetric sections
Multidomain Geometry
Split cells and fill voids to create multiple domains with different properties
Geometry Transformation
Manipulate geometries to preferred orientation and size by rotation, scaling, and translation
Modal Damping
Include damping in modal transient and frequency response simulations
See release notes for details on any of these features and corresponding functions.
