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أخواني في الله أحضرت لكم كتاب MATLAB Partial Differential Equation Toolbox - User ' s Guide
![كتاب MATLAB Partial Differential Equation Toolbox - User ' s Guide M_p_d_10](https://i.servimg.com/u/f61/15/36/74/14/m_p_d_10.jpg) و المحتوى كما يلي :
Getting Started 1 Partial Differential Equation Toolbox Product Description 1-2 Key Features 1-2 Equations You Can Solve Using PDE Toolbox . 1-3 Solve 2-D PDEs Using the PDE Modeler App 1-5 Tips . 1-5 Poisson’s Equation with Complex 2-D Geometry: PDE Modeler App . 1-7 Finite Element Method Basics 1-11 Deflection Analysis of Bracket 1-14 Heat Transfer in Block with Cavity 1-25 Setting Up Your PDE 2 Solve Problems Using PDEModel Objects 2-2 Geometry and Mesh Components . 2-4 2-D Geometry Creation at Command Line . 2-16 Three Elements of Geometry . 2-16 Basic Shapes . 2-16 Rectangle with Circular End Cap and Another Circular Excision . 2-17 Decomposed Geometry Data Structure 2-20 Parametrized Function for 2-D Geometry Creation . 2-22 Required Syntax . 2-22 Relation Between Parametrization and Region Labels . 2-22 Geometry Function for a Circle 2-23 Arc Length Calculations for a Geometry Function 2-24 Geometry Function Example with Subdomains and a Hole . 2-33 Nested Function for Geometry with Additional Parameters . 2-35 Geometry from polyshape 2-39 STL File Import 2-43 v ContentsSTEP File Import . 2-59 Geometry from Triangulated Mesh 2-63 3-D Geometry from a Finite Element Mesh . 2-63 2-D Multidomain Geometry . 2-64 Geometry from alphaShape 2-66 Cuboids, Cylinders, and Spheres 2-68 Sphere in Cube 2-75 3-D Multidomain Geometry from 2-D Geometry 2-79 Multidomain Geometry Reconstructed from Mesh 2-83 Put Equations in Divergence Form 2-87 Coefficient Matching for Divergence Form . 2-87 Boundary Conditions Can Affect the c Coefficient 2-88 Coefficient Conversion with Symbolic Math Toolbox 2-88 Some Equations Cannot Be Converted 2-89 f Coefficient for specifyCoefficients 2-90 c Coefficient for specifyCoefficients . 2-92 Overview of the c Coefficient . 2-92 Definition of the c Tensor Elements . 2-92 Some c Vectors Can Be Short . 2-94 Functional Form 2-104 m, d, or a Coefficient for specifyCoefficients . 2-107 Coefficients m, d, or a 2-107 Short m, d, or a vectors 2-107 Nonconstant m, d, or a . 2-108 View, Edit, and Delete PDE Coefficients . 2-111 View Coefficients . 2-111 Delete Existing Coefficients . 2-112 Change a Coefficient Assignment . 2-113 Set Initial Conditions 2-114 What Are Initial Conditions? . 2-114 Constant Initial Conditions 2-114 Nonconstant Initial Conditions . 2-114 Nodal Initial Conditions 2-115 Nonlinear System with Cross-Coupling Between Components . 2-117 Set Initial Condition for Model with Fine Mesh Using Solution Obtained with Coarser Mesh . 2-121 View, Edit, and Delete Initial Conditions . 2-123 View Initial Conditions . 2-123 Delete Existing Initial Conditions . 2-124 Change an Initial Conditions Assignment . 2-125 vi ContentsNo Boundary Conditions Between Subdomains . 2-126 Identify Boundary Labels . 2-128 Specify Boundary Conditions 2-129 Dirichlet Boundary Conditions . 2-129 Neumann Boundary Conditions 2-130 Mixed Boundary Conditions . 2-132 Nonconstant Boundary Conditions 2-132 Additional Arguments in Functions for Nonconstant Boundary Conditions 2-134 Solve PDEs with Constant Boundary Conditions 2-135 Specify Nonconstant Boundary Conditions . 2-139 Geometry and Mesh . 2-139 Scalar PDE Problem with Nonconstant Boundary Conditions 2-140 Anonymous Functions for Nonconstant Boundary Conditions 2-142 Additional Arguments 2-142 System of PDEs 2-143 Specify Nonconstant PDE Coefficients 2-146 Geometry and Mesh . 2-146 Function for Nonconstant Coefficient f . 2-146 Anonymous Function for a PDE Coefficient 2-148 Additional Arguments 2-148 View, Edit, and Delete Boundary Conditions 2-150 View Boundary Conditions 2-150 Delete Existing Boundary Conditions 2-152 Change a Boundary Conditions Assignment . 2-152 Generate Mesh 2-154 Find Mesh Elements and Nodes by Location 2-162 Assess Quality of Mesh Elements . 2-168 Mesh Data as [p,e,t] Triples . 2-172 Mesh Data . 2-175 Solving PDEs 3 von Mises Effective Stress and Displacements: PDE Modeler App 3-3 Clamped Square Isotropic Plate with Uniform Pressure Load . 3-7 Deflection of Piezoelectric Actuator . 3-11 viiDynamics of Damped Cantilever Beam . 3-21 Dynamic Analysis of Clamped Beam . 3-28 Reduced-Order Modeling Technique for Beam with Point Load . 3-33 Modal and Frequency Response Analysis for Single Part of Kinova Gen3 Robotic Arm . 3-40 Thermal Stress Analysis of Jet Engine Turbine Blade . 3-52 Finite Element Analysis of Electrostatically Actuated MEMS Device . 3-59 Deflection Analysis of Bracket 3-74 Vibration of Square Plate 3-85 Structural Dynamics of Tuning Fork . 3-90 Modal Superposition Method for Structural Dynamics Problem 3-99 Stress Concentration in Plate with Circular Hole 3-102 Thermal Deflection of Bimetallic Beam 3-110 Axisymmetric Thermal and Structural Analysis of Disc Brake . 3-119 Electrostatic Potential in Air-Filled Frame . 3-130 Electrostatic Potential in Air-Filled Frame: PDE Modeler App . 3-133 Electrostatic Analysis of Transformer Bushing Insulator . 3-135 Magnetic Flux Density in H-Shaped Magnet 3-141 Magnetic Flux Density in Electromagnet 3-146 Linear Elasticity Equations 3-156 Summary of the Equations of Linear Elasticity . 3-156 3D Linear Elasticity Problem 3-157 Plane Stress . 3-159 Plane Strain . 3-160 Magnetic Field in Two-Pole Electric Motor . 3-161 Magnetic Field in Two-Pole Electric Motor: PDE Modeler App . 3-166 Helmholtz Equation on Disk with Square Hole 3-170 Electrostatics and Magnetostatics 3-176 Electrostatics 3-176 Magnetostatics . 3-176 Magnetostatics with Permanent Magnets . 3-177 viii ContentsDC Conduction 3-178 Harmonic Electromagnetics . 3-179 Current Density Between Two Metallic Conductors 3-181 Skin Effect in Copper Wire with Circular Cross Section: PDE Modeler App 3-184 Current Density Between Two Metallic Conductors: PDE Modeler App 3-192 Heat Transfer Between Two Squares Made of Different Materials: PDE Modeler App 3-195 Temperature Distribution in Heat Sink 3-199 Create 2-D Geometry in PDE Modeler App 3-199 Extrude 2-D Geometry into 3-D Geometry of Heat Sink . 3-200 Perform Thermal Analysis . 3-203 Nonlinear Heat Transfer in Thin Plate 3-210 Poisson's Equation on Unit Disk: PDE Modeler App . 3-218 Poisson's Equation on Unit Disk . 3-224 Scattering Problem 3-232 Scattering Problem: PDE Modeler App 3-237 Minimal Surface Problem . 3-241 Minimal Surface Problem: PDE Modeler App . 3-247 Poisson's Equation with Point Source and Adaptive Mesh Refinement 3-249 Heat Transfer in Block with Cavity: PDE Modeler App . 3-254 Heat Transfer in Block with Cavity . 3-258 Heat Transfer Problem with Temperature-Dependent Properties . 3-262 Heat Conduction in Multidomain Geometry with Nonuniform Heat Flux 3-270 Inhomogeneous Heat Equation on Square Domain 3-277 Heat Distribution in Circular Cylindrical Rod 3-281 Thermal Analysis of Disc Brake 3-287 Heat Distribution in Circular Cylindrical Rod: PDE Modeler App . 3-295 Wave Equation on Square Domain 3-298 ixWave Equation on Square Domain: PDE Modeler App 3-302 Eigenvalues and Eigenmodes of L-Shaped Membrane 3-305 Eigenvalues and Eigenmodes of L-Shaped Membrane: PDE Modeler App 3-311 L-Shaped Membrane with Rounded Corner: PDE Modeler App 3-314 Eigenvalues and Eigenmodes of Square . 3-317 Eigenvalues and Eigenmodes of Square: PDE Modeler App . 3-322 Vibration of Circular Membrane . 3-325 Solution and Gradient Plots with pdeplot and pdeplot3D . 3-329 2-D Solution and Gradient Plots with MATLAB Functions . 3-338 3-D Solution and Gradient Plots with MATLAB Functions . 3-344 Types of 3-D Solution Plots Available in MATLAB . 3-344 2-D Slices Through 3-D Geometry . 3-344 Contour Slices Through 3-D Solution 3-347 Plots of Gradients and Streamlines 3-351 Dimensions of Solutions, Gradients, and Fluxes 3-356 PDE Modeler App 4 Open the PDE Modeler App . 4-2 2-D Geometry Creation in PDE Modeler App . 4-3 Create Basic Shapes . 4-3 Select Several Shapes 4-4 Rotate Shapes . 4-4 Create Complex Geometries . 4-4 Adjust Axes Limits and Grid . 4-5 Create Geometry with Rounded Corners 4-8 Specify Boundary Conditions in the PDE Modeler App 4-12 Specify Coefficients in PDE Modeler App . 4-14 Coefficients for Scalar PDEs 4-14 Coefficients for Systems of PDEs 4-16 Coefficients That Depend on Time and Space . 4-18 Specify Mesh Parameters in the PDE Modeler App . 4-24 Adjust Solve Parameters in the PDE Modeler App 4-26 Elliptic Equations 4-26 x ContentsParabolic Equations 4-28 Hyperbolic Equations . 4-29 Eigenvalue Equations . 4-29 Nonlinear Equations 4-30 Plot the Solution in the PDE Modeler App 4-31 Additional Plot Control Options 4-33 Tooltip Displays for Mesh and Plots 4-35 Functions #ماتلاب,#متلاب,#Matlab,
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