Introduction to Finite Element Analysis and Design

Nam-Ho Kim, PhD, is Professor in the Department of Mechanical and Aerospace Engineering at the University of Florida, where he has taught Finite Element Analysis and Design for 20 years. His research focuses on structural design optimization, sensitivity analysis, design under uncertainty, nonlinear structural mechanics, and related subjects. He has authored or co-authored several books and over 250 articles. Bhavani V. Sankar, PhD, is Professor in the Department of Mechanical and Aerospace Engineering at the University of Florida. He has published over 300 articles in journals and conference proceedings and is a Fellow of ASME, Founding Member and Fellow of the American Society for Composites, and Associate Fellow of the AIAA. He is a three-time recipient of the Bisplinghoff Memorial Teaching Award and a two-time recipient of the Florida Teaching Incentive Program Award. Ashok V. Kumar, PhD, is Associate Professor in the Department of Mechanical and Aerospace Engineering at the University of Florida, where he has taught both undergraduate and graduate-level finite element analysis courses. He has authored over 50 papers in journals and conference proceedings, and his research group has developed commercial finite element analysis software which enables mesh independent analysis.

• Preface xiAbout the Companion Website xv1 Direct Method—Springs, Bars, and Truss Elements 11.1 Illustration of the Direct Method 21.2 Uniaxial Bar Element 81.3 Plane Truss Elements 171.4 3D Truss Elements (Space Truss) 291.5 Thermal Loads and Thermal Strains 341.6 Finite Element Modeling Practice for Truss 411.7 Projects 481.8 Exercises 522 Finite Element Analysis of Beams and Frames 672.1 Review of Elementary Beam Theory 672.2 Finite Element Formulation for Beams 732.3 Plane Frame Elements 922.4 Buckling of Beams 992.5 Buckling of Frames 1102.6 Finite Element Modeling Practice for Beams 1122.7 Project 1172.8 Exercises 1193 Finite Elements for Heat Transfer Problems 1313.1 Introduction 1313.2 Fourier Heat Conduction Equation 1323.3 Finite Element Analysis—Direct Method 1343.4 Galerkin’s Method for Heat Conduction Problems 1403.5 Convection Boundary Conditions 1473.6 Isoparametric 1D Heat Transfer Elements 1543.7 2D Heat Transfer 1623.8 Three-Node Triangular Elements for 2D Heat Transfer 1683.9 Isoparametric Three-Node Triangular Heat Transfer Element 1773.10 Finite Element Modeling Practice for 2D Heat Transfer 1813.11 Exercises 1834 Review of Solid Mechanics 1894.1 Introduction 1894.2 Stress 1904.3 Strain 2034.4 Stress–Strain Relationship 2084.5 Boundary Value Problems 2124.6 Principle of Minimum Potential Energy for Plane Solids 2164.7 Principle of Virtual Work 2184.8 Failure Theories 2204.9 Safety Factor 2264.10 Exercises 2295 Finite Elements for 2D Solid Mechanics 2395.1 Introduction 2395.2 Types of 2D Problems 2405.3 Constant Strain Triangular (CST) Element 2425.4 Four-Node Rectangular Element 2565.5 Axisymmetric Element 2665.6 Finite Element Modeling Practice for Solids 2715.7 Project 2755.8 Exercises 2766 Isoparametric Finite Elements 2856.1 Introduction 2856.2 1D Isoparametric Elements 2866.3 Numerical Integration 2936.4 Timoshenko Beam Element Formulation 2956.5 2D Isoparametric Quadrilateral Elements 3046.6 Higher-Order Quadrilateral Elements 3196.7 Isoparametric Triangular Elements 3246.8 3D Isoparametric Elements 3306.9 Finite Element Modeling Practice for Isoparametric Elements 3356.10 Projects 3436.11 Exercises 3447 Plate and Shell Elements 3517.1 Introduction 3517.2 Plate Theories 3527.3 Shell Theories 3597.4 Principle of Virtual Work for Shell Elements 3617.5 Thin Plate Elements 3637.6 Thick Plate Elements 3707.7 Shell Elements 3787.8 Finite Element Modeling Practice for Plates and Shells 3837.9 Projects 3877.10 Exercises 3888 Finite Element Analysis for Dynamic Problems 3918.1 Introduction 3918.2 Dynamic Equation of Motion and Mass Matrix 3928.3 Natural Vibration: Natural Frequencies and Mode Shapes 3998.4 Forced Vibration: Direct Integration Approach 4078.5 Method of Mode Superposition 4208.6 Dynamic Analysis with Structural Damping 4268.7 Finite Element Modeling Practice for Dynamic Problems 4328.8 Exercises 4419 Finite Element Procedure and Modeling 4459.1 Introduction 4459.2 Finite Element Analysis Procedures 4459.3 Finite Element Modeling Issues 4679.4 Error Analysis and Convergence 4819.5 Project 4889.6 Exercises 48910 Structural Design Using Finite Elements 49510.1 Introduction 49510.2 Conservatism in Structural Design 49610.3 Intuitive Design: Fully Stressed Design 50310.4 Design Parameterization 50610.5 Parametric Study—Sensitivity Analysis 50910.6 Structural Optimization 51510.7 Projects 52910.8 Exercises 531Index 535