Preface xi About the Companion Website xv 1 Direct Method--Springs, Bars, and Truss Elements 1 1.1 Illustration of the Direct Method 2 1.2 Uniaxial Bar Element 8 1.3 Plane Truss Elements 17 1.4 3D Truss Elements (Space Truss) 29 1.5 Thermal Loads and Thermal Strains 34 1.6 Finite Element Modeling Practice for Truss 41 1.7 Projects 48 1.
8 Exercises 52 2 Finite Element Analysis of Beams and Frames 67 2.1 Review of Elementary Beam Theory 67 2.2 Finite Element Formulation for Beams 73 2.3 Plane Frame Elements 92 2.4 Buckling of Beams 99 2.5 Buckling of Frames 110 2.6 Finite Element Modeling Practice for Beams 112 2.7 Project 117 2.
8 Exercises 119 3 Finite Elements for Heat Transfer Problems 131 3.1 Introduction 131 3.2 Fourier Heat Conduction Equation 132 3.3 Finite Element Analysis--Direct Method 134 3.4 Galerkin''s Method for Heat Conduction Problems 140 3.5 Convection Boundary Conditions 147 3.6 Isoparametric 1D Heat Transfer Elements 154 3.7 2D Heat Transfer 162 3.
8 Three-Node Triangular Elements for 2D Heat Transfer 168 3.9 Isoparametric Three-Node Triangular Heat Transfer Element 177 3.10 Finite Element Modeling Practice for 2D Heat Transfer 181 3.11 Exercises 183 4 Review of Solid Mechanics 189 4.1 Introduction 189 4.2 Stress 190 4.3 Strain 203 4.4 Stress-Strain Relationship 208 4.
5 Boundary Value Problems 212 4.6 Principle of Minimum Potential Energy for Plane Solids 216 4.7 Principle of Virtual Work 218 4.8 Failure Theories 220 4.9 Safety Factor 226 4.10 Exercises 229 5 Finite Elements for 2D Solid Mechanics 239 5.1 Introduction 239 5.2 Types of 2D Problems 240 5.
3 Constant Strain Triangular (CST) Element 242 5.4 Four-Node Rectangular Element 256 5.5 Axisymmetric Element 266 5.6 Finite Element Modeling Practice for Solids 271 5.7 Project 275 5.8 Exercises 276 6 Isoparametric Finite Elements 285 6.1 Introduction 285 6.2 1D Isoparametric Elements 286 6.
3 Numerical Integration 293 6.4 Timoshenko Beam Element Formulation 295 6.5 2D Isoparametric Quadrilateral Elements 304 6.6 Higher-Order Quadrilateral Elements 319 6.7 Isoparametric Triangular Elements 324 6.8 3D Isoparametric Elements 330 6.9 Finite Element Modeling Practice for Isoparametric Elements 335 6.10 Projects 343 6.
11 Exercises 344 7 Plate and Shell Elements 351 7.1 Introduction 351 7.2 Plate Theories 352 7.3 Shell Theories 359 7.4 Principle of Virtual Work for Shell Elements 361 7.5 Thin Plate Elements 363 7.6 Thick Plate Elements 370 7.7 Shell Elements 378 7.
8 Finite Element Modeling Practice for Plates and Shells 383 7.9 Projects 387 7.10 Exercises 388 8 Finite Element Analysis for Dynamic Problems 391 8.1 Introduction 391 8.2 Dynamic Equation of Motion and Mass Matrix 392 8.3 Natural Vibration: Natural Frequencies and Mode Shapes 399 8.4 Forced Vibration: Direct Integration Approach 407 8.5 Method of Mode Superposition 420 8.
6 Dynamic Analysis with Structural Damping 426 8.7 Finite Element Modeling Practice for Dynamic Problems 432 8.8 Exercises 441 9 Finite Element Procedure and Modeling 445 9.1 Introduction 445 9.2 Finite Element Analysis Procedures 445 9.3 Finite Element Modeling Issues 467 9.4 Error Analysis and Convergence 481 9.5 Project 488 9.
6 Exercises 489 10 Structural Design Using Finite Elements 495 10.1 Introduction 495 10.2 Conservatism in Structural Design 496 10.3 Intuitive Design: Fully Stressed Design 503 10.4 Design Parameterization 506 10.5 Parametric Study--Sensitivity Analysis 509 10.6 Structural Optimization 515 10.7 Projects 529 10.
8 Exercises 531 Index 535.