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.
Using linear static analysis to compute displacement, stress, and strain under load, you can evaluate a component’s mechanical strength and behavior.
Mechanical components can resonate, which can result in deformation and potentially dangerous and damaging large-amplitude vibrations. Partial Differential Equation Toolbox™ lets you perform modal analysis to find natural frequencies and mode shapes to identify and prevent potential resonances.
For time-varying loads, you can perform transient dynamic simulation to compute displacement, velocity, acceleration, stress, and strain. You can plot or animate the deformed shapes and compute reaction forces.
Address challenges with thermal management by analyzing the temperature distributions of components based on material properties, external heat sources, and internal heat generation. Partial Differential Equation Toolbox lets you solve conduction-dominant heat transfer problems with convection and radiation occurring at the boundaries. You can perform steady-state and transient heat transfer analysis.
You can use Partial Differential Equation Toolbox to solve engineering problems described by second-order PDEs, including electrostatics, magnetostatics, diffusion, and other custom applications. For more information, see equations you can solve with the toolbox.
Partial Differential Equation Toolbox uses the finite element method to solve problems. A typical workflow consists of importing geometry; generating a mesh; defining the physics, including materials as well as boundary and initial conditions; and then solving and visualizing your results. The toolbox provides functions for each step in the workflow, allowing you to perform finite element analysis (FEA) in just a few lines of code.
The MATLAB® language makes it easy to customize, automate, and integrate your FEA applications. Partial Differential Equation Toolbox integrates with other MATLAB products, allowing you to build and share custom applications with MATLAB Compiler™, run design of experiments in parallel with Parallel Computing Toolbox™, and leverage high-fidelity simulation in Simulink® and Simscape™.
You can automatically generate a finite element mesh using triangular elements in 2D and tetrahedral elements in 3D. You can specify either piecewise linear or quadratic basis functions when meshing, depending on the required accuracy of your solution. You can inspect and analyze the mesh for quality and compute useful metrics like area or volume. For more information on generating finite element meshes, see Meshing.
You can use Partial Differential Equation Toolbox and MATLAB graphics to visualize your solution by creating plots and animations. You can plot the geometry, mesh, results, and derived and interpolated quantities. You can also create multiple subplots and easily customize plot properties.
Partial Differential Equation Toolbox provides you with solutions and their gradients at the mesh nodes and lets you interpolate them within the domain. MATLAB provides extensive functionality for further statistical postprocessing and data analysis.