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| Preface | |
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| Meet the Finite Element Method | |
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| What Is the Finite Element Method? | |
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| How the Finite Element Method Works | |
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| A Brief History of the Method | |
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| Range of Applications | |
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| Commercial Finite Element Software | |
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| The Future of the Finite Element Method | |
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| References | |
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| The Direct Approach: A Physical Interpretation | |
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| Introduction | |
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| Defining Elements and Their Properties | |
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| Assembling the Parts | |
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| Solver Technology | |
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| Closure | |
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| References | |
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| Problems | |
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| The Mathematical Approach: A Variational Interpretation | |
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| Introduction | |
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| Continuum Problems | |
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| Some Methods for Solving Continuum Problems | |
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| The Finite Element Method | |
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| Closure | |
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| References | |
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| Problems | |
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| The Mathematical Approach: A Generalized Interpretation | |
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| Introduction | |
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| Deriving Finite Element Equations from the Method of Weighted Residuals | |
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| Closure | |
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| References | |
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| Problems | |
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| Elements and Interpolation Functions | |
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| Introduction | |
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| Basic Element Shapes | |
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| Terminology and Preliminary Considerations | |
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| Generalized Coordinates and the Order of the Polynomial | |
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| Natural Coordinates | |
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| Interpolation Concepts in One Dimension | |
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| Internal Nodes--Condensation/Substructuring | |
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| Two-Dimensional Elements | |
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| Three-Dimensional Elements | |
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| Isoparametric Elements for C[superscript 0] Problems | |
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| Numerical Integration | |
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| Closure | |
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| References | |
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| Problems | |
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| Elasticity Problems | |
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| Introduction | |
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| General Formulation for Three-Dimensional Problems | |
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| Application to Plane Stress and Plane Strain | |
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| Application to Axisymmetric Stress Analysis | |
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| Application to Plate-Bending Problems | |
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| Three-Dimensional Problem | |
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| Introduction to Structural Dynamics | |
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| Closure | |
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| References | |
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| Problems | |
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| General Field Problems | |
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| Introduction | |
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| Equilibrium Problems | |
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| Eigenvalue Problems | |
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| Propagation Problem | |
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| Solving the Discretized Time-Dependent Equations | |
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| Closure | |
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| References | |
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| Problems | |
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| Heat Transfer Problems | |
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| Introduction | |
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| Conduction | |
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| Conduction with Surface Radiation | |
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| Convective-Diffusion Equation | |
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| Free and Forced Convection | |
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| Closure | |
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| References | |
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| Problems | |
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| Fluid Mechanics Problems | |
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| Introduction | |
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| Inviscid Incompressible Flow | |
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| Viscous Incompressible Flow without Inertia | |
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| Viscous Incompressible Flow with Inertia | |
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| Compressible Flow | |
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| Closure | |
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| References | |
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| Problems | |
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| Boundary Conditions, Mesh Generation, and Other Practical Considerations | |
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| Introduction | |
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| Physical Singularities | |
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| Benchmark Problems | |
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| Symmetry | |
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| Dimensional Analysis | |
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| Mesh Generation | |
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| Lumped Mass versus Consistent Mass | |
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| Modeling Fasteners | |
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| Connecting Rod Analysis | |
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| Crankshaft and Flywheel Analysis | |
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| Disc Brake Analysis | |
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| Closure | |
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| References | |
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| Problems | |
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| Finite Elements in Design | |
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| Introduction | |
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| Design Optimization | |
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| Finite Element--Based Optimal Design | |
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| Design Sensitivity Analysis | |
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| Examples of Design Sensitivity Analysis | |
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| Case Study: Finite Element-Based Design | |
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| Closure | |
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| References | |
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| Problems | |
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| Matrices | |
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| Definitions | |
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| Special Types of Square Matrices | |
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| Matrix Operations | |
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| Special Matrix Products | |
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| Matrix Transpose | |
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| Quadratic Forms | |
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| Matrix Inverse | |
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| Matrix Partitioning | |
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| The Calculus of Matrices | |
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| Norms | |
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| Variational Calculus | |
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| Introduction | |
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| Calculus--The Minima of a Function | |
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| Variational Calculus--The Minima of Functionals | |
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| Basic Equations from Linear Elasticity Theory | |
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| Introduction | |
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| Stress Components | |
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| Strain Components | |
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| Generalized Hooke's Law (Constitutive Equations) | |
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| Static Equilibrium Equations | |
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| Compatibility Conditions | |
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| Differential Equations for Displacements | |
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| Minimum Potential Energy Principle | |
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| Plane Strain and Plane Stress | |
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| Thermal Effects | |
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| Thin-Plate Bending | |
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| References | |
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| Basic Equations from Fluid Mechanics | |
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| Introduction | |
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| Definitions and Concepts | |
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| Laws of Motion | |
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| Stream Functions and Vorticity | |
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| Potential Flow | |
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| Viscous Incompressible Flow | |
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| Boundary Layer Flow | |
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| References | |
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| Basic Equations from Heat Transfer | |
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| Introduction | |
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| Conduction | |
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| Convection | |
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| Radiation | |
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| Heat Transfer Units | |
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| References | |
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| Index | |