Title The finite element method : basic concepts and applications with MATLAB, MAPLE, and COMSOL / Darrell W. Pepper, Juan C. Heinrich

Edition Third edition Published Boca Raton : CRC Press, Taylor & Francis Group, CRC Press is an imprint of the Taylor & Francis Group, an informa business, [2017] ©2017

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Description 1 online resource (xviii, 609 pages) : illustrations (black and white) Series Series in Computational and Physical Processes in Mechanics and Thermal Sciences Series in computational and physical processes in mechanics and thermal sciences. Contents Machine generated contents note: 1.1. Background -- 1.2. Short History -- 1.3. Orientation -- 1.4. Closure -- References -- 2.1. Background -- 2.2. Classical Solutions -- 2.3. The "Weak" Statement -- 2.4. Closure -- Exercises -- References -- 3.1. Background -- 3.2. Shape Functions -- 3.2.1. Linear Elements -- 3.2.2. Quadratic Elements -- 3.2.3. Cubic Elements -- 3.3. Steady Conduction Equation -- 3.3.1. Galerkin Formulation -- 3.3.2. Variable Conduction And Boundary Convection -- 3.4. Axisymmetric Heat Conduction -- 3.5. Natural Coordinate System -- 3.6. Time Dependence -- 3.6.1. Spatial Discretization -- 3.6.2. Time Discretization -- 3.7. Matrix Formulation -- 3.8. Solution Methods -- 3.9. Closure -- Problems -- References -- 4.1. Background -- 4.2. The Mesh -- 4.3. Shape Functions -- 4.3.1. Linear Shape Functions -- 4.3.2. Quadratic Shape Functions -- 4.4. Area Coordinates -- 4.5. Numerical Integration -- 4.6. Conduction In A Triangular Element -- 4.7. Steady-State Conduction With Boundary Convection -- 4.8. The Axisymmetric Conduction Equation -- 4.9. The Quadratic Triangular Element -- 4.10. Time-Dependent Diffusion Equation -- 4.11. Bandwidth -- 4.12. Mass Lumping -- 4.13. Closure -- Exercises -- References -- 5.1. Background -- 5.2. Element Mesh -- 5.3. Shape Functions -- 5.3.1. Bilinear Rectangular Element -- 5.3.2. Quadratic Rectangular Element -- 5.4. Natural Coordinate System -- 5.5. Numerical Integration Using Gaussian Quadratures -- 5.6. Steady-State Conduction Equation -- 5.7. Steady-State Conduction With Boundary Convection -- 5.8. The Quadratic Quadrilateral Element -- 5.9. Time-Dependent Diffusion -- 5.10. Computer Program Exercises -- 5.11. Closure -- Exercises -- References -- 6.1. Background -- 6.2. Natural Coordinate System -- 6.3. Shape Functions -- 6.3.1. Bilinear Quadrilateral -- 6.3.2. Eight-Noded Quadratic Quadrilateral -- 6.3.3. Linear Triangle -- 6.3.4. Quadratic Triangle -- 6.3.5. Directional Cosines -- 6.4. The Element Matrices -- 6.5. Inviscid Flow Example -- 6.6. Closure -- Exercises -- References -- 7.1. Background -- 7.2. Element Mesh -- 7.3. Shape Functions -- 7.3.1. Tetrahedron -- 7.3.2. Hexahedron -- 7.4. Numerical Integration -- 7.5. A One-Element Heat Conduction Problem -- 7.5.1. Tetrahedron -- 7.5.2. Hexahedron -- 7.6. Time-Dependent Heat Conduction With Radiation And Convection -- 7.6.1. Radiation -- 7.6.2. Shape Factors -- 7.7. Closure -- Exercises -- References -- 8.1. Background -- 8.2. Two-Dimensional Elasticity: Stress/Strain -- 8.3. Galerkin Approximation -- 8.4. Potential Energy -- 8.5. Thermal Stresses -- 8.6. Three-Dimensional Solid Elements -- 8.7. Closure -- Exercises -- References -- 9.1. Background -- 9.2. Potential Flow -- 9.3. Convective Transport -- 9.4. Nonlinear Convective Transport -- 9.5. Groundwater Flow -- 9.6. Lubrication -- 9.7. Closure -- Exercises -- References -- 10.1. Background -- 10.2. Viscous Incompressible Flow With Heat Transfer -- 10.3. The Penalty Function Algorithm -- 10.4. Equal Order: Projection Method -- 10.5. Application To Free And Forced Convection -- 10.6. Closure -- Exercises -- References -- 11.1. Introduction -- 11.2. One-Dimensional BEM -- 11.3. Two-Dimensional BEM -- 11.3.1. Constant Elements -- 11.3.2. Linear Elements -- 11.4. Three-Dimensional BEM -- 11.5. Dual Reciprocity Method -- 11.6. Closure -- Exercises -- References -- 12.1. Background -- 12.2. History Of Mems -- 12.3. Radial Basis Functions -- 12.3.1. Global Versus Local RBFs -- 12.4. The Kansa Approach -- 12.5. Implementation Of The Mem -- 12.5.1. 1-D Formulation -- 12.5.2. 2-D Formulation -- 12.6. Smooth Particle Hydrodynamics -- 12.7. Closure -- Exercises -- References Summary This self-explanatory guide introduces the basic fundamentals of the Finite Element Method in a clear manner using comprehensive examples. Beginning with the concept of one-dimensional heat transfer, the first chapters include one-dimensional problems that can be solved by inspection. The book progresses through more detailed two-dimensional elements to three-dimensional elements, including discussions on various applications, and ending with introductory chapters on the boundary element and meshless methods, where more input data must be provided to solve problems. Emphasis is placed on the development of the discrete set of algebraic equations. The example problems and exercises in each chapter explain the procedure for defining and organizing the required initial and boundary condition data for a specific problem, and computer code listings in MATLAB and MAPLE are included for setting up the examples within the text, including COMSOL files Notes Previous edition: 2005 Bibliography Includes bibliographical references and index Notes Description based on print version record Subject Finite element method. TECHNOLOGY & ENGINEERING / Engineering (General) TECHNOLOGY & ENGINEERING / Reference. Finite element method Form Electronic book Author Heinrich, Juan C., author. ISBN 9781315395081 1315395088 9781315395098 1315395096 9781315395074 131539507X 9781315395104 131539510X 9781315369402 1315369400

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