دانلود کتاب MATLAB Partial Differential Equation Toolbox™ User's Guide

فهرست مطالب :

Getting Started Partial Differential Equation Toolbox Product Description Key Features Equations You Can Solve Using PDE Toolbox Solve 2-D PDEs Using the PDE Modeler App Tips Poisson’s Equation with Complex 2-D Geometry: PDE Modeler App Finite Element Method Basics Deflection Analysis of Bracket Heat Transfer in Block with Cavity Setting Up Your PDE Solve Problems Using PDEModel Objects Geometry and Mesh Components 2-D Geometry Creation at Command Line Three Elements of Geometry Basic Shapes Rectangle with Circular End Cap and Another Circular Excision Decomposed Geometry Data Structure Parametrized Function for 2-D Geometry Creation Required Syntax Relation Between Parametrization and Region Labels Geometry Function for a Circle Arc Length Calculations for a Geometry Function Geometry Function Example with Subdomains and a Hole Nested Function for Geometry with Additional Parameters Geometry from polyshape STL File Import STEP File Import Geometry from Triangulated Mesh 3-D Geometry from a Finite Element Mesh 2-D Multidomain Geometry Geometry from alphaShape Cuboids, Cylinders, and Spheres Sphere in Cube 3-D Multidomain Geometry from 2-D Geometry Multidomain Geometry Reconstructed from Mesh Put Equations in Divergence Form Coefficient Matching for Divergence Form Boundary Conditions Can Affect the c Coefficient Coefficient Conversion with Symbolic Math Toolbox Some Equations Cannot Be Converted f Coefficient for specifyCoefficients c Coefficient for specifyCoefficients Overview of the c Coefficient Definition of the c Tensor Elements Some c Vectors Can Be Short Functional Form m, d, or a Coefficient for specifyCoefficients Coefficients m, d, or a Short m, d, or a vectors Nonconstant m, d, or a View, Edit, and Delete PDE Coefficients View Coefficients Delete Existing Coefficients Change a Coefficient Assignment Set Initial Conditions What Are Initial Conditions? Constant Initial Conditions Nonconstant Initial Conditions Nodal Initial Conditions Nonlinear System with Cross-Coupling Between Components Set Initial Condition for Model with Fine Mesh Using Solution Obtained with Coarser Mesh View, Edit, and Delete Initial Conditions View Initial Conditions Delete Existing Initial Conditions Change an Initial Conditions Assignment No Boundary Conditions Between Subdomains Identify Boundary Labels Specify Boundary Conditions Dirichlet Boundary Conditions Neumann Boundary Conditions Mixed Boundary Conditions Nonconstant Boundary Conditions Additional Arguments in Functions for Nonconstant Boundary Conditions Solve PDEs with Constant Boundary Conditions Specify Nonconstant Boundary Conditions Geometry and Mesh Scalar PDE Problem with Nonconstant Boundary Conditions Anonymous Functions for Nonconstant Boundary Conditions Additional Arguments System of PDEs Specify Nonconstant PDE Coefficients Geometry and Mesh Function for Nonconstant Coefficient f Anonymous Function for a PDE Coefficient Additional Arguments View, Edit, and Delete Boundary Conditions View Boundary Conditions Delete Existing Boundary Conditions Change a Boundary Conditions Assignment Generate Mesh Find Mesh Elements and Nodes by Location Assess Quality of Mesh Elements Mesh Data as [p,e,t] Triples Mesh Data Solving PDEs von Mises Effective Stress and Displacements: PDE Modeler App Clamped Square Isotropic Plate with Uniform Pressure Load Deflection of Piezoelectric Actuator Dynamics of Damped Cantilever Beam Dynamic Analysis of Clamped Beam Reduced-Order Modeling Technique for Beam with Point Load Modal and Frequency Response Analysis for Single Part of Kinova Gen3 Robotic Arm Thermal Stress Analysis of Jet Engine Turbine Blade Finite Element Analysis of Electrostatically Actuated MEMS Device Deflection Analysis of Bracket Vibration of Square Plate Structural Dynamics of Tuning Fork Modal Superposition Method for Structural Dynamics Problem Stress Concentration in Plate with Circular Hole Thermal Deflection of Bimetallic Beam Axisymmetric Thermal and Structural Analysis of Disc Brake Electrostatic Potential in Air-Filled Frame Electrostatic Potential in Air-Filled Frame: PDE Modeler App Electrostatic Analysis of Transformer Bushing Insulator Magnetic Flux Density in H-Shaped Magnet Magnetic Flux Density in Electromagnet Linear Elasticity Equations Summary of the Equations of Linear Elasticity 3D Linear Elasticity Problem Plane Stress Plane Strain Magnetic Field in Two-Pole Electric Motor Magnetic Field in Two-Pole Electric Motor: PDE Modeler App Helmholtz Equation on Disk with Square Hole Electrostatics and Magnetostatics Electrostatics Magnetostatics Magnetostatics with Permanent Magnets DC Conduction Harmonic Electromagnetics Current Density Between Two Metallic Conductors Skin Effect in Copper Wire with Circular Cross Section: PDE Modeler App Current Density Between Two Metallic Conductors: PDE Modeler App Heat Transfer Between Two Squares Made of Different Materials: PDE Modeler App Temperature Distribution in Heat Sink Create 2-D Geometry in PDE Modeler App Extrude 2-D Geometry into 3-D Geometry of Heat Sink Perform Thermal Analysis Nonlinear Heat Transfer in Thin Plate Poisson's Equation on Unit Disk: PDE Modeler App Poisson's Equation on Unit Disk Scattering Problem Scattering Problem: PDE Modeler App Minimal Surface Problem Minimal Surface Problem: PDE Modeler App Poisson's Equation with Point Source and Adaptive Mesh Refinement Heat Transfer in Block with Cavity: PDE Modeler App Heat Transfer in Block with Cavity Heat Transfer Problem with Temperature-Dependent Properties Heat Conduction in Multidomain Geometry with Nonuniform Heat Flux Inhomogeneous Heat Equation on Square Domain Heat Distribution in Circular Cylindrical Rod Thermal Analysis of Disc Brake Heat Distribution in Circular Cylindrical Rod: PDE Modeler App Wave Equation on Square Domain Wave Equation on Square Domain: PDE Modeler App Eigenvalues and Eigenmodes of L-Shaped Membrane Eigenvalues and Eigenmodes of L-Shaped Membrane: PDE Modeler App L-Shaped Membrane with Rounded Corner: PDE Modeler App Eigenvalues and Eigenmodes of Square Eigenvalues and Eigenmodes of Square: PDE Modeler App Vibration of Circular Membrane Solution and Gradient Plots with pdeplot and pdeplot3D 2-D Solution and Gradient Plots with MATLAB Functions 3-D Solution and Gradient Plots with MATLAB Functions Types of 3-D Solution Plots Available in MATLAB 2-D Slices Through 3-D Geometry Contour Slices Through 3-D Solution Plots of Gradients and Streamlines Dimensions of Solutions, Gradients, and Fluxes PDE Modeler App Open the PDE Modeler App 2-D Geometry Creation in PDE Modeler App Create Basic Shapes Select Several Shapes Rotate Shapes Create Complex Geometries Adjust Axes Limits and Grid Create Geometry with Rounded Corners Specify Boundary Conditions in the PDE Modeler App Specify Coefficients in PDE Modeler App Coefficients for Scalar PDEs Coefficients for Systems of PDEs Coefficients That Depend on Time and Space Specify Mesh Parameters in the PDE Modeler App Adjust Solve Parameters in the PDE Modeler App Elliptic Equations Parabolic Equations Hyperbolic Equations Eigenvalue Equations Nonlinear Equations Plot the Solution in the PDE Modeler App Additional Plot Control Options Tooltip Displays for Mesh and Plots Functions Visualize PDE Results adaptmesh addCell addFace addVertex addVoid AnalyticGeometry applyBoundaryCondition area assema assemb assembleFEMatrices assempde cellEdges cellFaces BodyLoadAssignment BoundaryCondition CoefficientAssignment createpde createPDEResults csgdel decsg DiscreteGeometry dst idst EigenResults ElectromagneticModel electromagneticBC ElectromagneticBCAssignment electromagneticProperties ElectromagneticMaterialAssignment electromagneticSource ElectromagneticSourceAssignment ElectrostaticResults MagnetostaticResults HarmonicResults ConductionResults evaluate evaluateCGradient evaluateGradient evaluateHeatFlux evaluateHeatRate evaluatePrincipalStrain evaluatePrincipalStress evaluateReaction evaluateStrain evaluateStress evaluateTemperatureGradient evaluateVonMisesStress FEMesh extrude faceEdges facesAttachedToEdges findBodyLoad findBoundaryConditions findCoefficients findElectromagneticBC findElectromagneticProperties findElectromagneticSource findElements findHeatSource findInitialConditions findNodes findStructuralBC findStructuralIC findStructuralProperties findThermalBC findThermalIC findThermalProperties generateMesh GeometricInitialConditions GeometricStructuralICs GeometricThermalICs NodalInitialConditions NodalStructuralICs NodalThermalICs geometryFromEdges geometryFromMesh HeatSourceAssignment hyperbolic importGeometry initmesh internalHeatSource interpolateAcceleration interpolateDisplacement interpolateElectricField interpolateElectricFlux interpolateCurrentDensity interpolateHarmonicField interpolateElectricPotential interpolateMagneticField interpolateMagneticFlux interpolateMagneticPotential interpolateSolution interpolateStrain interpolateStress interpolateTemperature interpolateVelocity interpolateVonMisesStress jigglemesh linearize linearizeInput linearizeOutput meshQuality meshToPet multicuboid multicylinder multisphere nearestEdge nearestFace parabolic pdearcl pdecgrad pdecirc pdecont pdeeig pdeellip pdegplot pdegrad pdeInterpolant pdeintrp pdejmps pdemesh PDEModel pdenonlin pdeplot pdeplot3D pdepoly pdeprtni pderect pdesdp pdesde pdesdt pdesmech PDESolverOptions pdesurf PDE Modeler pdetrg pdetriq pdeviz PDEVisualization poimesh poisolv reconstructSolution reduce ReducedStructuralModel ReducedThermalModel refinemesh rotate scale setInitialConditions solve solvepde solvepdeeig specifyCoefficients ModalStructuralResults FrequencyStructuralResults StaticStructuralResults TransientStructuralResults structuralBC StructuralBC structuralIC structuralDamping findStructuralDamping StructuralDampingAssignment StructuralMaterialAssignment structuralBodyLoad structuralBoundaryLoad StructuralModel structuralProperties structuralSEInterface StructuralSEIAssignment StationaryResults SteadyStateThermalResults ThermalBC ThermalMaterialAssignment ThermalModel thermalProperties translate TimeDependentResults TransientThermalResults ModalThermalResults thermalBC thermalIC tri2grid volume wbound wgeom