The Trefftz finite and boundary element method
By: Qing-Hua Qin.
Publisher: WIT Press
Published: 2000
Place of publication: Southampton; Boston
Language: eng
Number of pages: 282
Subjects: Finite element method.; Boundary element methods.
Notes: Includes bibliographical references.
Table of contents: title: Machine generated contents note: Chapter 1 Introduction 1; title: 11 Finite element technique 1; title: 12 Shape functions and element stiffness matrix 7; title: 13 Brief historical background 15; title: 14 Basic relationships in engineering problems 16; title: 15 Modified variational principles 21; title: 16 The concept of T-complete solution 23; title: 17 Comparison of T-elements with conventional finite elements 24; title: 18 Comparison of T-elements with boundary elements 35; title: References 38; title: Chapter 2 Potential Problems 43; title: 21 Introduction 43; title: 22 Statement of the problem 44; title: 23 T-complete functions 45; title: 24 Assumed fields 46; title: 25 Generation of element matrix equation 49; title: 26 Rank condition 53; title: 27 Special purpose functions 54; title: 28 Sensitivity to mesh distortion 57; title: 29 Orthotropic case 57; title: 210 The Helmholtz equation 60; title: 211 HT-element with boundary 'traction' frame 62; title: 212 Frameless T-elements 67; title: References 71; title: Chapter 3 Linear Elastostatics 73; title: 31 Introduction 73; title: 32 Linear theory of elasticity 73; title: 33 Assumed fields in plane elasticity 79; title: 34 T-complete functions 81; title: 35 Variational formulations 84; title: 36 Element stiffness equation 86; title: 37 Special-purpose elements 88; title: 38 p-extension approach 96; title: 39 Three-dimensional elasticity 97; title: 310 Numerical examples 98; title: References 101; title: Chapter 4 Thin Plates 103; title: 41 Introduction 103; title: 42 Thin plate theory 103; title: 43 Assumed field 107; title: 44 T-complete functions and particular solutions 109; title: 45 Variational formulations for plate bending 111; title: 46 Generation of element stiffness matrix 113; title: 47 p-method elements 115; title: 48 Special purpose functions 116; title: 49 Extension to thin plates on elastic foundation 119; title: 410 Two alternative plate bending p-elements 122; title: 411 Numerical examples and assessment 126; title: References 136; title: Chapter 5 Thick Plates 139; title: 51 Introduction 139; title: 52 Basic equations for Reissner-Mindlin plate theory 140; title: 53 Assumed fields and particular solution 141; title: 54 Variational formulation for HT thick plate elements 149; title: 55 Implementation of the new family of HT elements 151; title: 56 A 12 DOF quadrilateral element free of shear locking 153; title: 57 Extension to thick plates on elastic foundation 157; title: 58 Sensitivity to mesh distortion 160; title: 59 Numerical assessment 160; title: References 170; title: Chapter 6 Transient Heat Conduction 173; title: 61 Introduction 173; title: 62 Elements of heat conduction 174; title: 63 Time step formula 174; title: 64 Element matrix formulations 175; title: 65 T-complete functions and particular solutions 179; title: 66 Numerical examples 179; title: References 184; title: Chapter 7 Geometrically Nonlinear Analysis of; title: Plate Bending Problems 187; title: 71 Introduction 187; title: 72 Basic equations of nonlinear thin plate bending 187; title: 73 Assumed fields and Trefftz functions 191; title: 74 Particular solutions 194; title: 75 Modified Variational principle 195; title: 76 Element matrix 197; title: 77 Iterative scheme 199; title: 78 Extension to post-buckling thin plates on elastic foundation 200; title: 79 Geometrically nonlinear analysis of thick plates 202; title: 710 Numerical examples 210; title: References 216; title: Chapter 8 Elastoplasticity 219; title: 81 Introduction 219; title: 82 Time discretization 219; title: 83 Basic relations 220; title: 84 Assumed fields 223; title: 85 Constraints on the approximation functions 224; title: 86 Finite element equilibrium and compatibility equations 225; title: 87 Finite element equations 226; title: 88 Finite element governing system 229; title: References 230; title: Chapter 9 Dynamics of Plate Bending Problems 231; title: 91 Introduction 231; title: 92 Basic equations 231; title: 93 Time-stepping formulation 232; title: 94 Numerical examples 235; title: References 238; title: Chapter 10 Trefftz Boundary Element Method 239; title: 101 Introduction 239; title: 102 Potential problems 239; title: 103 Plane elasticity 250; title: 104 Thin plate bending 256; title: 105 Moderately thick plates 260; title: References 265; title: Appendix A Numerical Integration 267; title: Appendix B Matrix Algebra and Calculus 271.