Finite element analysis (FEA) has become the dominant tool of analysis in many industrial fields of engineering, particularly in mechanical and aerospace engineering. This process requires significant computational work divided into several distinct phases. What Every Engineer Should Know About Computational Techniques of Finite Element Analysis offers a concise, self-contained treatment of FEA and all of the tools needed for efficient use and practical implementation. This book provides you with a walk-through of the process from the physical model to the computed solution. Based on the author's thirty years of practical experience in finite element analysis in the shipbuilding, aerospace, and automobile industries, it describes the transformation of the physical problem into a mathematical model, reduction of the model to a more efficient, numerically solvable form, and the solution of the problem using specific computational techniques. The author discusses time and frequency domain solutions as used in practice, as well as the representation of the computed results. What Every Engineer Should Know About Computational Techniques of Finite Element Analysis serves as a to-the-point guide to using or implementing FEA for both beginners and everyday users who must apply the finite element method to your daily work. The techniques can be easily executed in most available FEA software packages.

Dr. Louis Komzsik is a graduate of the Technical University of Budapest, Hungary. Having worked for more than 35 years in the industry, he is currently Chief Numerical Analyst in the Office of Architecture and Technology at Siemens PLM Software. He has researched, implemented, and applied many computational techniques for finite element analysis during his career and this book is the outcome of his considerable experience. Dr. Komzsik's book on the Lanczos method has been translated into Japanese, Hungarian, Korean, and Chinese. He is also the author of Approximation Techniques for Engineers (2006) and Applied Calculus of Variations for Engineers (2008), both published by CRC Press.

Preface to the second edition	p. xiii
Preface to the first edition	p. xv
Acknowledgments	p. xvii
Numerical Model Generation	p. 1
Finite Element Analysis	p. 3
Solution of boundary value problems	p. 3
Finite element shape functions	p. 6
Finite element basis functions	p. 9
Assembly of finite element matrices	p. 12
Element matrix generation	p. 15
Local to global coordinate transformation	p. 19
A linear quadrilateral finite element	p. 20
Quadratic finite elements	p. 26
References	p. 29
Finite Element Model Generation	p. 31
Bezier spline approximation	p. 31
Bezier surfaces	p. 37
B-spline technology	p. 40
Computational example	p. 43
NURBS objects	p. 48
Geometric model discretization	p. 50
Delaunay mesh generation	p. 51
Model generation case study	p. 54
References	p. 57
Modeling of Physical Phenomena	p. 59
Lagrange's equations of motion	p. 59
Continuum mechanical systems	p. 61
Finite element analysis of elastic continuum	p. 63
A tetrahedral finite element	p. 65
Equation of motion of mechanical system	p. 69
Transformation to frequency domain	p. 71
References	p. 74
Constraints and Boundary Conditions	p. 75
The concept of multi-point constraints	p. 76
The elimination of multi-point constraints	p. 79
An axial bar element	p. 82
The concept of single-point constraints	p. 85
The elimination of single-point constraints	p. 86
Rigid body motion support	p. 88
Constraint augmentation approach	p. 90
References	p. 92
Singularity Detection of Finite Element Models	p. 93
Local singularities	p. 93
Global singularities	p. 97
Massless degrees of freedom	p. 99
Massless mechanisms	p. 100
Industrial case studies	p. 102
References	p. 104
Coupling Physical Phenomena	p. 105
Fluid-structure interaction	p. 105
A hexahedral finite element	p. 106
Fluid finite elements	p. 109
Coupling structure with compressible fluid	p. 111
Coupling structure with incompressible fluid	p. 112
Structural acoustic case study	p. 113
References	p. 115
Computational Reduction Techniques	p. 117
Matrix Factorization and Linear Systems	p. 119
Finite element matrix reordering	p. 119
Sparse matrix factorization	p. 122
Multi-frontal factorization	p. 124
Linear system solution	p. 126
Distributed factorization and solution	p. 127
Factorization and solution case studies	p. 130
Iterative solution of linear systems	p. 134
Preconditioned iterative solution technique	p. 137
References	p. 139
Static Condensation	p. 141
Single-level, single-component condensation	p. 141
Computational example	p. 144
Single-level, multiple-component condensation	p. 147
Multiple-level static condensation	p. 152
Static condensation case study	p. 155
References	p. 158
Real Spectral Computations	p. 159
Spectral transformation	p. 159
Lanczos reduction	p. 161
Generalized eigenvalue problem	p. 164
Eigensolution computation	p. 166
Distributed eigenvalue computation	p. 168
Dense eigenvalue analysis	p. 172
Householder reduction technique	p. 175
Normal modes analysis case studies	p. 177
References	p. 181
Complex Spectral Computations	p. 183
Complex spectral transformation	p. 183
Biorthogonal Lanczos reduction	p. 184
Implicit operator multiplication	p. 186
Recovery of physical solution	p. 188
Solution evaluation	p. 190
Reduction to Hessenberg form	p. 191
Rotating component application	p. 192
Complex modal analysis case studies	p. 196
References	p. 199
Dynamic Reduction	p. 201
Single-level, single-component dynamic reduction	p. 201
Accuracy of dynamic reduction	p. 203
Computational example	p. 206
Single-level, multiple-component dynamic reduction	p. 208
Multiple-level dynamic reduction	p. 210
Multi-body analysis application	p. 212
References	p. 215
Component Mode Synthesis	p. 217
Single-level, single-component modal synthesis	p. 217
Mixed boundary component mode reduction	p. 219
Computational example	p. 222
Single-level, multiple-component modal synthesis	p. 225
Multiple-level modal synthesis	p. 228
Component mode synthesis case study	p. 230
References	p. 232
Engineering Solution Computations	p. 235
Modal Solution Technique	p. 237
Modal solution	p. 237
Truncation error in modal solution	p. 239
The method of residual flexibility	p. 241
The method of mode acceleration	p. 245
Coupled modal solution application	p. 246
Modal contributions and energies	p. 247
References	p. 250
Transient Response Analysis	p. 251
The central difference method	p. 251
The Newmark method	p. 252
Starting conditions and time step changes	p. 254
Stability of time integration techniques	p. 255
Transient response case study	p. 258
State-space formulation	p. 259
References	p. 262
Frequency Domain Analysis	p. 263
Direct and modal frequency response analysis	p. 263
Reduced-order frequency response analysis	p. 264
Accuracy of reduced-order solution	p. 267
Frequency response case study	p. 268
Enforced motion application	p. 269
References	p. 271
Nonlinear Analysis	p. 273
Introduction to nonlinear analysis	p. 273
Geometric nonlinearity	p. 275
Newton-Raphson methods	p. 278
Quasi-Newton iteration techniques	p. 282
Convergence criteria	p. 284
Computational example	p. 285
Nonlinear dynamics	p. 287
References	p. 288
Sensitivity and Optimization	p. 289
Design sensitivity	p. 289
Design optimization	p. 290
Planar bending of the bar	p. 294
Computational example	p. 297
Eigenfunction sensitivities	p. 302
Variational analysis	p. 304
References	p. 308
Engineering Result Computations	p. 309
Displacement recovery	p. 309
Stress calculation	p. 311
Nodal data interpolation	p. 312
Level curve computation	p. 314
Engineering analysis case study	p. 316
References	p. 319
Annotation	p. 321
List of Figures	p. 323
List of Tables	p. 325
Index	p. 327
Closing Remarks	p. 331
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