Category: Matlab pde toolbox examples

Documentation Help Center. This example analyses the temperature distribution of a disc brake. Disc brakes absorb the translational mechanical energy through friction and transform it into the thermal energy, which then dissipates. The transient thermal analysis of a disc brake is critical because the friction and braking performance decreases at high temperatures.

Therefore, disc brakes must not exceed a given temperature limit during operation. Perform a highly detailed simulation of the brake pad moving around the disc. Because the computational cost is high, this part of the example only simulates one half revolution 25 ms. Simulate a circular brake pad moving around the disc. This detailed simulation over a short timescale models the heat source as a point moving around the disc. Generate a fine mesh with a small target maximum element edge length.

The resulting mesh has more than nodes degrees of freedom. Specify the boundary conditions. All the faces are exposed to air, so there will be free convection. Model the moving heat source by using a function handle that defines the thermal load as a function of space and time. For the definition of the movingHeatSource function, see the Heat Source Functions section at the bottom of this page.

The animation function visualizes the solution for all time steps. To play the animation, use this command:. Because the heat diffusion time is much longer than the period of a revolution, you can simplify the heat source for the long simulation. Now find the disc temperatures for a longer period of time. Because the heat does not have time to diffuse during a revolution, it is reasonable to approximate the heat source with a static heat source in the shape of the path of the brake pad.

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Compute the heat flow applied to the disc as a function of time. Specify the boundary condition as a function handle. For the definition of the ringHeatSource function, see the Heat Source Functions section at the bottom of this page. To play the animation, use the following command:.Sign in to comment.

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PDE TOOLBOX: PLOT HEAT FLUX AT 3D NODAL POSITIONS

Support Answers MathWorks. Search MathWorks. MathWorks Answers Support. Open Mobile Search. Scarica una trial. You are now following this question You will see updates in your activity feed. You may receive emails, depending on your notification preferences. Abed Alnaif on 8 Dec Vote 0. Commented: Mario Buchely on 13 Apr at Accepted Answer: Bill Greene. I've been trying to solve a non-linear, heat-equation-type system of PDE's using the 'pdepe' function, with only one dimension in space.

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However, for many sets of parameter values, the solver exhibits unstable behaviour oscillations, etc. I think that my problem demands a more sophisticated solver, due to nonlinearities and discontinuities.

Hence, I am now trying to use the PDE Toolbox, hoping that it would be able to handle my problem, since it has an adaptive mesh algorithm, etc. However, I was unable to figure out how to use the PDE Toolbox for one-dimensional problems, nor was I able to find any examples of this. Is it possible to use the PDE Toolbox to solve one-dimensional problems? I'm find with using the command-line interface I don't necessarily need to use the GUI.Documentation Help Center. Create a PDEModel object using createpde.

It is 1 for scalar problems. Number of equations, Nreturned as a positive integer. You create boundary conditions using the applyBoundaryCondition function. AnalyticGeometry Properties object for 2-D geometry. You create this geometry using the geometryFromEdges function. DiscreteGeometry Properties object for 3-D geometry.

You create this geometry using the importGeometry function or the geometryFromMesh function. Mesh for solution, returned as an FEMesh Properties object.

matlab pde toolbox examples

You create the mesh using the generateMesh function. Indicator if model is time-dependent, returned as 1 true or 0 false. The property is true when the m or d coefficient is nonzero, and is false otherwise. See specifyCoefficients.

matlab pde toolbox examples

In case of GeometricInitialConditionsfor time-dependent problems, you must give one or two initial conditions: one if the m coefficient is zero, and two if the m coefficient is nonzero. For nonlinear stationary problems, you can optionally give an initial solution that solvepde uses to start its iterations.

matlab pde toolbox examples

See setInitialConditions. In case of NodalInitialConditionsyou use the results of previous analysis to set the initial conditions or initial guess.

The geometry and mesh of the previous analysis and current model must be the same. Include a torus geometry, zero Dirichlet boundary conditions, coefficients for Poisson's equation, and the default mesh. A modified version of this example exists on your system. Do you want to open this version instead?

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Create a PDE model container specifying the number of equations in your model. Defining 2-D or 3-D geometry and mesh it using triangular and tetrahedral elements with linear or quadratic basis functions. Specify the coefficients, boundary and initial conditions. Use function handles to specify non-constant values.

Solve and plot the results at nodal locations or interpolate them to custom locations. Specify Boundary Conditions. Use functions when you cannot express your boundary conditions by constant input arguments.

Set Initial Conditions. Set initial conditions for time-dependent problems or initial guess for nonlinear stationary problems. Plot 2-D Solutions and Their Gradients.

Plot 3-D Solutions and Their Gradients. Dimensions of Solutions, Gradients, and Fluxes. Dimensions of stationary, time-dependent, and eigenvalue results at mesh nodes and arbitrary locations. Eigenvalues and Eigenmodes of Square. Eigenvalues and Eigenmodes of L-Shaped Membrane. Use command-line functions to find the eigenvalues and the corresponding eigenmodes of an L-shaped membrane.

Put Equations in Divergence Form. Finite Element Method Basics. Description of the use of the finite element method to approximate a PDE solution using a piecewise linear function. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:.

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Solutions at Nodal and Custom Locations. PDE Model Properties. Legacy Workflow. View, Edit, and Delete Initial Conditions.

Partial Differential Equation Toolbox

Dimensions of Solutions, Gradients, and Fluxes Dimensions of stationary, time-dependent, and eigenvalue results at mesh nodes and arbitrary locations. Eigenvalue Problems Eigenvalues and Eigenmodes of Square Find the eigenvalues and eigenmodes of a square domain.

Eigenvalues and Eigenmodes of L-Shaped Membrane Use command-line functions to find the eigenvalues and the corresponding eigenmodes of an L-shaped membrane.The PDE Toolbox is a tool to solve partial differential equations PDE by making it easy to input the 2-D domain, specify the PDE coefficients and boundary conditions, and numerically solve a finite element discretization using piecewise linear elements.

Problems can be completely specified and solved within a graphical user interface GUI called pdetool or the GUI can be used to specify only some of the data such as the domain, boundary conditions, and mesh description. From the Options menu, select Axes Limits Select Grid Spacing if you wish to change the grid spacing the default is 0.

Domains are constructed by the addition and subtraction of primitive domains such as rectangles, polygons, and ellipses. A similar procedure is used for rectangles. To draw a polygon, click on the polygon button and then form each side by dragging the mouse with held left button.

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To form the desired domain, type in a formula in the Set formula box above the displayed region to combine the primitives by addition or subtraction.

To save this domain for later use, select Export geometry description from the Draw menu and click OK in the box. This exports the geometry data, set formulas, and labels with the names gd sf ns unless you change them.

As we shall see later, this form of the geometry called the Constructive Solid Geometry model must be processed into the "decomposed geometry" before it can be used in several MATLAB commands. However, it is easier to wait until the boundary conditions are specified and then export both the boundary conditions and decomposed geometry simultaneously.

Enter boundary mode by clicking on the "d Omega" button or selecting Boundary Mode from the Boundary menu. Select one boundary segment by clicking on it, or several boundary segments by holding down the Shift key and clicking on the desired segments, or all the boundary segments by selecting Select All from the Edit menu.

To input the boundary conditions, for this segment or group of segments, select Specify Boundary Conditions Neumann boundary conditions are input by first clicking on the Neumann box and then specifying the coefficients g and q.

The general form of the boundary condition appears at the top of the box n is the unit outward normal and c is a coefficient in the PDE. This exports the decomposed geometry data and boundary data with the names g b unless you change them. From the Mesh menu, select Parameters to optionally choose a desired maximum edge size, where Inf gives the coarsest possible mesh. To generate an initial mesh, click on the triangle button or select Initialize Mesh from the Mesh menu.

This exports the triangle vertices, triangle edges, and triangle ordering with the names: p e t unless you change them. Note that if you wish to compare the computed and exact solution at the vertices or compute various norms of the error, this information will be needed. Click on the subdivided triangle or select Refine Mesh from the Mesh menu to get a refined mesh. The default refinement method is regular. To change to longest edge, select Parameters and then longest from the Mesh menu.

Enter the desired maximum number of triangles or maximum number of refinement steps. Various types of plots are available. Select Parameters from the Plot menu. First, you may wish to save the decomposed geometry g in a file in your directory named, for example, prob1g.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 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. 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.

Find natural frequencies and mode shapes to identify and prevent potential resonances, and simulate dynamic behavior of a structure using its frequency responses. Analyze temperature distributions of components to address thermal management challenges. Find temperature distributions and other thermal characteristics under time-varying thermal loads.

Solve second-order linear and nonlinear PDEs for stationary, time-dependent, and eigenvalue problems. Reconstruct 2D and 3D geometry from imported STL or mesh data, or create simple parameterized shapes using geometric primitives. Generate finite element mesh using triangular elements in 2D and tetrahedral elements in 3D.

Inspect and analyze mesh quality to assess accuracy of results. Compute derived and interpolated data from results as well as create plots and animations. 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. Analyze solutions and its gradients at mesh nodes and other interpolated locations. 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.

Speed up simulations by simplifying 3D solids of revolution by analyzing only the 2D axisymmetric sections. See release notes for details on any of these features and corresponding functions.

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matlab pde toolbox examples

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Solving one-dimensional PDE's using the PDE Toolbox

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