An edition of The Trefftz finite and boundary element method
(2000)
The Trefftz finite and boundary element method
by Qing-Hua Qin
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Table of Contents
Machine generated contents note: Chapter 1 Introduction 1
11 Finite element technique 1
12 Shape functions and element stiffness matrix 7
13 Brief historical background 15
14 Basic relationships in engineering problems 16
15 Modified variational principles 21
16 The concept of T-complete solution 23
17 Comparison of T-elements with conventional finite elements 24
18 Comparison of T-elements with boundary elements 35
References 38
Chapter 2 Potential Problems 43
21 Introduction 43
22 Statement of the problem 44
23 T-complete functions 45
24 Assumed fields 46
25 Generation of element matrix equation 49
26 Rank condition 53
27 Special purpose functions 54
28 Sensitivity to mesh distortion 57
29 Orthotropic case 57
210 The Helmholtz equation 60
211 HT-element with boundary 'traction' frame 62
212 Frameless T-elements 67
References 71
Chapter 3 Linear Elastostatics 73
31 Introduction 73
32 Linear theory of elasticity 73
33 Assumed fields in plane elasticity 79
34 T-complete functions 81
35 Variational formulations 84
36 Element stiffness equation 86
37 Special-purpose elements 88
38 p-extension approach 96
39 Three-dimensional elasticity 97
310 Numerical examples 98
References 101
Chapter 4 Thin Plates 103
41 Introduction 103
42 Thin plate theory 103
43 Assumed field 107
44 T-complete functions and particular solutions 109
45 Variational formulations for plate bending 111
46 Generation of element stiffness matrix 113
47 p-method elements 115
48 Special purpose functions 116
49 Extension to thin plates on elastic foundation 119
410 Two alternative plate bending p-elements 122
411 Numerical examples and assessment 126
References 136
Chapter 5 Thick Plates 139
51 Introduction 139
52 Basic equations for Reissner-Mindlin plate theory 140
53 Assumed fields and particular solution 141
54 Variational formulation for HT thick plate elements 149
55 Implementation of the new family of HT elements 151
56 A 12 DOF quadrilateral element free of shear locking 153
57 Extension to thick plates on elastic foundation 157
58 Sensitivity to mesh distortion 160
59 Numerical assessment 160
References 170
Chapter 6 Transient Heat Conduction 173
61 Introduction 173
62 Elements of heat conduction 174
63 Time step formula 174
64 Element matrix formulations 175
65 T-complete functions and particular solutions 179
66 Numerical examples 179
References 184
Chapter 7 Geometrically Nonlinear Analysis of
Plate Bending Problems 187
71 Introduction 187
72 Basic equations of nonlinear thin plate bending 187
73 Assumed fields and Trefftz functions 191
74 Particular solutions 194
75 Modified Variational principle 195
76 Element matrix 197
77 Iterative scheme 199
78 Extension to post-buckling thin plates on elastic foundation 200
79 Geometrically nonlinear analysis of thick plates 202
710 Numerical examples 210
References 216
Chapter 8 Elastoplasticity 219
81 Introduction 219
82 Time discretization 219
83 Basic relations 220
84 Assumed fields 223
85 Constraints on the approximation functions 224
86 Finite element equilibrium and compatibility equations 225
87 Finite element equations 226
88 Finite element governing system 229
References 230
Chapter 9 Dynamics of Plate Bending Problems 231
91 Introduction 231
92 Basic equations 231
93 Time-stepping formulation 232
94 Numerical examples 235
References 238
Chapter 10 Trefftz Boundary Element Method 239
101 Introduction 239
102 Potential problems 239
103 Plane elasticity 250
104 Thin plate bending 256
105 Moderately thick plates 260
References 265
Appendix A Numerical Integration 267
Appendix B Matrix Algebra and Calculus 271.
Edition Notes
Includes bibliographical references.
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| December 4, 2010 | Edited by Open Library Bot | Added subjects from MARC records. |
| April 28, 2010 | Edited by Open Library Bot | Linked existing covers to the work. |
| December 8, 2009 | Created by ImportBot | add works page |