The Trefftz finite and boundary element method
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-co...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Southampton u.a.
WIT Press
2000
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| Online Zugang: | Inhaltsverzeichnis Inhaltstext |
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Tag hinzufügen | Zusammenfassung: | 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 |
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| Beschreibung: | Literaturangaben |
| Beschreibung: | 282 S. graph. Darst. 24 cm |
| ISBN: | 1853128554 1-85312-855-4 |