Finite Element Method (FEM) is one of the numerical methods of solving differential equations that describe many engineering problems. This new book covers the basic theory of FEM and includes appendices on each of the main FEA programs as reference. It introduces the concepts so that engineers can use the method efficiently and interpret the results properly. They'll learn about one-dimensional finite elements, including truss and beam elements, as well as two and three dimensional finite elements. Numerous examples are also included using ANSYS, ABAQUS, NASTRAN, Pro/Engineer, and I-DEAS. This approach will help engineers develop a thorough understanding of the theory behind FEM as well as its application.

Preface	p. vii
Mathematical Preliminaries	p. 1
Vectors and Matrices	p. 1
Vector-Matrix Calculus	p. 3
Matrix Equations	p. 8
Eigen Values and Eigen Vectors	p. 8
Quadratic Forms	p. 12
Maxima and Minima of Functions	p. 13
Exercise	p. 14
Stress-Strain Analysis	p. 17
Stress	p. 17
Strain	p. 30
Stress-Strain Relations	p. 35
Boundary Value Problems	p. 39
Failure Theories	p. 43
Safety Factor	p. 49
Exercise	p. 52
Uniaxial Bar and Truss Elements-Direct Method	p. 60
Illustration of the Direct Method	p. 61
Uniaxial Bar Element	p. 66
Plane Truss Elements	p. 73
Three-Dimensional Truss Elements (Space Truss)	p. 83
Thermal Stresses	p. 87
Projects	p. 94
Exercise	p. 98
Weighted Residual and Energy Methods for One-Dimensional Problems	p. 108
Exact vs. Approximate Solution	p. 108
Galerkin Method	p. 109
Higher-Order Differential Equations	p. 114
Finite Element Approximation	p. 117
Formal Procedure	p. 124
Energy Methods	p. 129
Exercise	p. 138
Finite Element Analysis of Beams and Frames	p. 143
Review of Elementary Beam Theory	p. 143
Rayleigh-Ritz Method	p. 148
Finite Element Interpolation	p. 153
Finite Element Equation for the Beam Element	p. 158
Bending Moment and Shear Force Distribution	p. 166
Plane Frame	p. 171
Project	p. 175
Exercise	p. 176
Finite Elements for Heat Transfer Problems	p. 185
Introduction	p. 185
Fourier Heat Conduction Equation	p. 186
Finite Element Analysis - Direct Method	p. 188
Galerkin Method for Heat Conduction Problems	p. 194
Convection Boundary Conditions	p. 200
Exercise	p. 207
Finite Elements for Plane Solids	p. 211
Introduction	p. 211
Types of Two-Dimensional Problems	p. 211
Principle of Minimum Potential Energy	p. 214
Constant Strain Triangular (CST) Element	p. 216
Four-Node Rectangular Element	p. 229
Four-Node Iso-Parametric Quadrilateral Element	p. 237
Numerical Integration	p. 248
Project	p. 253
Exercise	p. 254
Finite Element Procedures and Modeling	p. 261
Finite Element Analysis Procedures	p. 261
Finite Element Modeling Techniques	p. 281
Project	p. 291
Exercise	p. 292
Structural Design Using Finite Elements	p. 297
Introduction	p. 297
Safety Margin in Design	p. 298
Intuitive Design: Fully-Stressed Design	p. 301
Design Parameterization	p. 304
Parameter Study - Sensitivity Analysis	p. 307
Structural Optimization	p. 313
Project: Design Optimization of a Bracket	p. 325
Exercise	p. 327
Finite Element Analysis Using Pro/Engineer	p. 333
Introduction	p. 333
Getting Start	p. 333
Plate with a Hole Analysis	p. 334
Design Sensitivity Analysis/Parameter Study	p. 339
Design Optimization	p. 341
Finite Element Analysis Using NEi Nastran	p. 343
Introduction	p. 343
Getting Start	p. 343
Plate with a Hole Analysis	p. 343
Static Analysis of Beams	p. 350
Examples in the text	p. 356
Finite Element Analysis Using ANSYS	p. 363
Introduction	p. 363
Getting Start	p. 364
Static Analysis of a Corner Bracket	p. 365
Examples in the Text	p. 381
Finite Element Analysis Using MATLAB Toolbox	p. 391
Finite Element Analysis of Bar and Truss	p. 391
Finite Element Analysis Using Frame Elements	p. 403
Finite Element Analysis Using Plane Solid Elements	p. 408
Index	p. 417
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