What Every Engineer Should Know About Computational Techniques of Finite Element Analysis

by Komzsik, Louis

• ISBN13: 9780849335631
• ISBN10: 0849335639
• Format: Hardcover
• Copyright: 2005-03-01
• Publisher: CRC

Summary

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.

Table of Contents

Preface	ix
About the Author	xi
List of Figures	xvii
List of tables	xix
Acknowledgments	xxi
I Numerical Model Generation	1	(82)
1 Finite Element Analysis	3	(24)
1.1 Solution of boundary value problems	3	(3)
1.2 Finite element shape functions	6	(2)
1.3 Finite element basis functions	8	(3)
1.4 Assembly of finite element matrices	11	(3)
1.5 Element matrix generation	14	(4)
1.6 Local to global coordinate transformation	18	(1)
1.7 A quadrilateral finite element	19	(6)
References	25	(2)
2 Finite Element Model Generation	27	(16)
2.1 Spline approximation	27	(6)
2.2 Geometric modeling objects	33	(4)
2.3 Geometric model discretization	37	(2)
2.4 Delaunay mesh generation	39	(2)
References	41	(2)
3 Modeling of Physical Phenomena	43	(16)
3.1 Lagrange's equations of motion	43	(2)
3.2 Continuum mechanical systems	45	(2)
3.3 Finite element analysis of elastic continuum	47	(2)
3.4 A tetrahedral finite element	49	(4)
3.5 Equation of motion of mechanical system	53	(2)
3.6 Transformation to frequency domain	55	(2)
References	57	(2)
4 Constraints and Boundary Conditions	59	(14)
4.1 The concept of multi-point constraints	60	(3)
4.2 The elimination of multi-point constraints	63	(3)
4.3 An axial bar element	66	(3)
4.4 The concept of single-point constraints	69	(1)
4.5 The elimination of single-point constraints	70	(2)
References	72	(1)
5 Singularity Detection of Finite Element Models	73	(10)
5.1 Local singularities	73	(4)
5.2 Global singularities	77	(2)
5.3 Massless degrees of freedom	79	(1)
5.4 Industrial case studies	80	(2)
References	82	(1)
II Computational Reduction Techniques	83	(98)
6 Matrix Factorization and Linear System Solution	85	(16)
6.1 Finite element matrix reordering	85	(3)
6.2 Sparse matrix factorization	88	(2)
6.3 Multi-frontal factorization	90	(2)
6.4 Linear system solution	92	(1)
6.5 Distributed factorization and solution	93	(3)
6.6 Factorization case study	96	(3)
References	99	(2)
7 Static Condensation	101	(16)
7.1 Single-level, single-component condensation	101	(3)
7.2 Computational example	104	(1)
7.3 Single-level, multiple-component condensation	105	(4)
7.4 Multiple-level static condensation	109	(4)
7.5 Static condensation case study	113	(3)
References	116	(1)
8 Spectral Computations	117	(30)
8.1 Spectral transformation	117	(2)
8.2 Lanczos reduction	119	(3)
8.3 Generalized eigenvalue problem	122	(2)
8.4 Eigenvalue computation	124	(2)
8.5 Distributed eigenvalue computation	126	(4)
8.6 Normal modes analysis case study	130	(3)
8.7 Complex spectral computation	133	(3)
8.8 Complex modes analysis case study	136	(2)
8.9 Dense eigenvalue analysis	138	(3)
8.10 Householder reduction techniques	141	(1)
8.11 Tridiagonal reduction	142	(2)
8.12 Reduction to Hessenberg form	144	(1)
References	145	(2)
9 Dynamic Reduction	147	(16)
9.1 Single-level, single-component dynamic reduction	147	(2)
9.2 Accuracy of dynamic reduction	149	(3)
9.3 Computational example	152	(2)
9.4 Single-level, multiple-component dynamic reduction	154	(2)
9.5 Multiple-level dynamic reduction	156	(3)
9.6 Multi-body analysis application	159	(1)
References	160	(3)
10 Component Modal Synthesis	163	(18)
10.1 Single-level, single-component modal synthesis	163	(2)
10.2 Mixed boundary component mode reduction	165	(3)
10.3 Computational example	168	(3)
10.4 Single-level, multiple-component modal synthesis	171	(3)
10.5 Multiple-level modal synthesis	174	(2)
10.6 Component modal synthesis case study	176	(2)
References	178	(3)
III Engineering Solution Computations	181	(78)
11 Modal Solution Technique	183	(12)
11.1 Modal reduction	183	(2)
11.2 Truncation error in modal reduction	185	(1)
11.3 The method of residual flexibility	186	(3)
11.4 The method of mode acceleration	189	(1)
11.5 Coupled modal solution application	190	(3)
References	193	(2)
12 Transient Response Analysis	195	(10)
12.1 The central difference method	195	(1)
12.2 The Newmark method	196	(2)
12.3 Starting conditions and time step changes	198	(1)
12.4 Stability of time integration techniques	199	(3)
12.5 Transient solution case study	202	(2)
References	204	(1)
13 Frequency Domain Analysis	205	(8)
13.1 Direct and modal frequency response analysis	205	(1)
13.2 Reduced-order frequency response analysis	206	(3)
13.3 Accuracy of reduced-order solution	209	(1)
13.4 Frequency response case study	210	(1)
References	211	(2)
14 Nonlinear Analysis	213	(16)
14.1 Introduction to nonlinear analysis	213	(4)
14.2 Newton-Raphson methods	217	(2)
14.3 Quasi-Newton iteration techniques	219	(3)
14.4 Convergence criteria	222	(1)
14.5 Computational example	223	(2)
14.6 Nonlinear dynamics	225	(2)
References	227	(2)
15 Sensitivity and Optimization	229	(20)
15.1 Design sensitivity	229	(1)
15.2 Design optimization	230	(4)
15.3 Planar bending of the bar	234	(3)
15.4 Computational example	237	(5)
15.5 Eigenfunction sensitivities	242	(2)
15.6 Variational analysis	244	(3)
References	247	(2)
16 Engineering Result Computations	249	(10)
16.1 Displacement recovery	249	(2)
16.2 Stress calculation	251	(1)
16.3 Nodal data interpolation	251	(3)
16.4 Level curve computation	254	(2)
16.5 Engineering results case study	256	(1)
References	257	(2)
Closing Remarks	259	(2)
Annotation	261	(2)
Index	263