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Full Description
A clear and accessible overview of the Finite Element Method
The finite element method (FEM), which involves solutions to partial differential equations and integro-differential equations, is a powerful tool for solving structural mechanics and fluid mechanics problems. FEM results in versatile computer programs with flexible applications, usable with minimal training to solve practical problems in a variety of engineering and design contexts. Introduction to Finite Element Analysis and Design offers a comprehensive yet readable overview of both theoretical and practical elements of FEM. With a greater focus on design aspects than most comparable volumes, it's an invaluable introduction to a key suite of software and design tools. The third edition has been fully updated to reflect the latest research and applications.
Readers of the third edition of Introduction to Finite Element Analysis and Design will find:
50% more exercise problems than the previous edition, with an accompanying solutions manual for instructors
A brand-new chapter on plate and shell finite elements
Tutorials for commercial finite element software, including MATLAB, ANSYS, ABAQUS, and NASTRAN
Introduction to Finite Element Analysis and Design is ideal for advanced undergraduate students in finite element analysis- or design-related courses, as well as for researchers and design engineers looking for self-guided tools.
Contents
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
