Introduction to Finite Element Analysis and Design

NAM-HO KIM, PHD is a professor in the Department of Mechanical & Aerospace Engineering at the University of Florida, USA. His research interests are in computational mechanics and design optimization, in particular, nonlinear solid mechanics and design under uncertainty. BHAVANI V. SANKAR, PHD is a professor in the Department of Mechanical & Aerospace Engineering at the University of Florida, USA. His research interests are in mechanics of composite materials and structures, in particular, micromechanics and fracture mechanics. ASHOK V. KUMAR, PHD is an Associate Professor in the Department of Mechanical & Aerospace Engineering at the University of Florida, USA. His research focus is in the area of computational methods and design optimization.

• Preface ixAbout the Companion Website xi1 Direct Method – Springs, Bars, and Truss Elements 11.1 Illustration of the Direct Method 21.2 Uniaxial Bar Element 71.3 Plane Truss Elements 151.4 Three-Dimensional Truss Elements (Space Truss) 271.5 Thermal Stresses 321.6 Finite Element Modeling Practice for Truss 391.7 Projects 451.8 Exercises 492 Weighted Residual Methods for One-Dimensional Problems 632.1 Exact vs. Approximate Solution 632.2 Galerkin Method 672.3 Higher-Order Differential Equations 722.4 Finite Element Approximation 752.5 Energy Methods 892.6 Exercises 993 Finite Element Analysis of Beams and Frames 1073.1 Review of Elementary Beam Theory 1073.2 Rayleigh-Ritz Method 1123.3 Finite Element Formulation for Beams 1173.4 Plane Frame Elements 1363.5 Buckling of Beams 1423.6 Buckling of Frames 1543.7 Finite Element Modeling Practice for Beams 1573.8 Project 1623.9 Exercises 1634 Finite Elements for Heat Transfer Problems 1754.1 Introduction 1754.2 Fourier Heat Conduction Equation 1764.3 Finite Element Analysis – Direct Method 1784.4 Galerkin’s Method for Heat Conduction Problems 1844.5 Convection Boundary Conditions 1914.6 Two-Dimensional Heat Transfer 1984.7 3-Node Triangular Elements for Two-Dimensional Heat Transfer 2044.8 Finite Element Modeling Practice for 2-D Heat Transfer 2134.9 Exercises 2155 Review of Solid Mechanics 2215.1 Introduction 2215.2 Stress 2225.3 Strain 2345.4 Stress–Strain Relationship 2405.5 Boundary Value Problems 2445.6 Principle of Minimum Potential Energy for Plane Solids 2495.7 Failure Theories 2505.8 Safety Factor 2565.9 Exercises 2596 Finite Elements for Two-Dimensional Solid Mechanics 2696.1 Introduction 2696.2 Types of Two-Dimensional Problems 2696.3 Constant Strain Triangular (CST) Element 2726.4 Four–Node Rectangular Element 2866.5 Axisymmetric Element 2966.6 Finite Element Modeling Practice for Solids 3006.7 Project 3056.8 Exercises 3067 Isoparametric Finite Elements 315 7.1 Introduction 3157.2 One-Dimensional Isoparametric Elements 3167.3 Two-Dimensional Isoparametric Quadrilateral Element 3267.4 Numerical Integration 3377.5 Higher-Order Quadrilateral Elements 3437.6 Isoparametric Triangular Elements 3497.7 Three-Dimensional Isoparametric Elements 3557.8 Finite Element Modeling Practice for Isoparametric Elements 3597.9 Projects 3687.10 Exercises 3698 Finite Element Analysis for Dynamic Problems 3778.1 Introduction 3778.2 Dynamic Equation of Motion and Mass Matrix 3788.3 Natural Vibration: Natural Frequencies and Mode Shapes 3848.4 Forced Vibration: Direct Integration Approach 3928.5 Method of Mode Superposition 4048.6 Dynamic Analysis with Structural Damping 4108.7 Finite Element Modeling Practice for Dynamic Problems 4148.8 Exercises 4239 Finite Element Procedure and Modeling 4279.1 Introduction 4279.2 Finite Element Analysis Procedures 4279.3 Finite Element Modeling Issues 4469.4 Error Analysis and Convergence 4609.5 Project 4669.6 Exercises 46710 Structural Design Using Finite Elements 47310.1 Introduction 47310.2 Conservatism in Structural Design 47410.3 Intuitive Design: Fully Stressed Design 48010.4 Design Parameterization 48410.5 Parametric Study – Sensitivity Analysis 48610.6 Structural Optimization 49110.7 Projects 50510.8 Exercises 507Appendix Mathematical Preliminaries 511A.1 Vectors and Matrices 511A.2 Vector-Matrix Calculus 514A.3 Matrix Equations and Solution 518A.4 Eigenvalues and Eigenvectors 524A.5 Quadratic Forms 528A.6 Maxima and Minima of Functions 529A.7 Exercises 530Index 533