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| Introduction | |
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| Background | |
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| Short History | |
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| Orientation | |
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| Closure | |
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| References | |
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| The Method of Weighted Residuals and Galerkin Approximations | |
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| Background | |
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| Classical Solutions | |
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| The "Weak" Statement | |
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| Closure | |
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| Exercises | |
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| References | |
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| The Finite Element Method in One Dimension | |
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| Background | |
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| Shape Functions | |
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| Linear Elements | |
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| Quadratic Elements | |
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| Cubic Elements | |
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| Steady Conduction Equation | |
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| Galerkin Formulation | |
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| Variable Conduction and Boundary Convection | |
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| Axisymmetric Heat Conduction | |
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| Natural Coordinate System | |
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| Time Dependence | |
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| Spatial Discretization | |
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| Time Discretization | |
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| Matrix Formulation | |
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| Solution Methods | |
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| Closure | |
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| Exercises | |
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| References | |
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| The Two-Dimensional Triangular Element | |
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| Background | |
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| The Mesh | |
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| Shape Functions (Linear, Quadratic) | |
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| Linear Shape Functions | |
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| Quadratic Shape Functions | |
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| Area Coordinates | |
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| Numerical Integration | |
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| Conduction in a Triangular Element | |
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| Steady-State Conduction with Boundary Convection | |
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| The Axisymmetric Conduction Equation | |
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| The Quadratic Triangular Element | |
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| Time-Dependent Diffusion Equation | |
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| Bandwidth | |
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| Mass Lumping | |
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| Closure | |
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| Exercises | |
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| References | |
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| The Two-Dimensional Quadrilateral Element | |
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| Background | |
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| Element Mesh | |
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| Shape Functions | |
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| Bilinear Rectangular Element | |
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| Quadratic Rectangular Element | |
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| Natural Coordinate System | |
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| Numerical Integration Using Gaussian Quadratures | |
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| Steady-State Conduction Equation | |
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| Steady-State Conduction with Boundary Convection | |
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| The Quadratic Quadrilateral Element | |
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| Time-Dependent Diffusion | |
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| Computer Program Exercises | |
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| Closure | |
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| Exercises | |
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| References | |
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| Isoparametric Two-Dimensional Elements | |
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| Background | |
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| Natural Coordinate System | |
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| Shape Functions | |
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| Bilinear Quadrilateral | |
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| Eight-Noded Quadratic Quadrilateral | |
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| Linear Triangle | |
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| Quadratic Triangle | |
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| Directional Cosines | |
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| The Element Matrices | |
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| Inviscid Flow Example | |
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| Closure | |
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| Exercises | |
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| References | |
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| The Three-Dimensional Element | |
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| Background | |
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| Element Mesh | |
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| Shape Functions | |
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| Tetrahedron | |
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| Hexahedron | |
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| Numerical Integration | |
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| A One-Element Heat Conduction Problem | |
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| Tetrahedron | |
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| Hexahedron | |
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| Time-Dependent Heat Conduction with Radiation and Convection | |
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| Radiation | |
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| Shape Factors | |
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| Closure | |
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| Exercises | |
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| References | |
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| Finite Elements in Solid Mechanics | |
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| Background | |
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| Two-Dimensional Elasticity-Stress Strain | |
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| Galerkin Approximation | |
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| Potential Energy | |
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| Thermal Stresses | |
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| Three-Dimensional Solid Elements | |
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| Closure | |
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| Exercises | |
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| References | |
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| Applications to Convective Transport | |
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| Background | |
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| Potential Flow | |
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| Convective Transport | |
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| Nonlinear Convective Transport | |
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| Groundwater Flow | |
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| Lubrication | |
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| Closure | |
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| Exercises | |
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| References | |
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| Introduction to Viscous Fluid Flow | |
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| Background | |
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| Viscous Incompressible Flow with Heat Transfer | |
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| The Penalty Function Algorithm | |
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| Application to Natural Convection | |
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| Closure | |
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| Exercises | |
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| References | |
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| Appendices | |
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| Matrix Algebra | |
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| Addition/Subtraction of Matrices | |
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| Multiplication of Matrices | |
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| Determinant of a Matrix | |
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| Inverse of a Matrix | |
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| Derivative of a Matrix | |
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| Transpose of a Matrix | |
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| Units | |
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| Thermophysical Properties of Some Common Materials | |
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| Dimensionless Groups | |
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| Computer Programs | |
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| Source Codes | |
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| Index | |