Boundary Element Programming in Mechanics,9780521773591

Boundary Element Programming in Mechanics

by
ISBN13: 9780521773591
ISBN10: 0521773598
Format: Multimedia
Pub. Date: 2002-03-11
Publisher(s): Cambridge University Press
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Summary

This monograph describes the application of boundary element methods (BEM) in solid mechanics, beginning with basic theory and then explaining the numerical implementation of BEM in nonlinear stress analysis. In addition, the authors have developed state-of-the-art BEM source code, available for the first time on a CD-ROM included with the book.

Author Biography

Xiao-Wei Gao is Research Associate, Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe. He was formerly Associate Professor, Institute of Applied Mechanics, Ningxia University, People's Republic of China. Dr. Gao is an authority on nonlinear boundary element analysis and is currently developing BEM techniques for commercial aerospace applications Trevor G. Davies is Senior Lecturer, Glasgow University. Dr. Davies's primary expertise is in numerical analysis of nonlinear and dynamic soil-structure interaction using boundary element methods. He was one of the first researchers to tackle the problem of 3D nonlinear boundary element analysis during the late 1970s. He has published extensively and has co-edited the book Boundary Element Techniques in Geomechanics

Table of Contents

Preface xiii
Legal Matters xv
PART I. LINEAR PROBLEMS
Introduction
3(13)
Introduction
3(1)
A Note on Programming
3(2)
Mathematical Preliminaries
5(7)
Historical Sketch
12(3)
Approximate Methods
12(1)
BEM in Solid Mechanics
13(1)
BEM in Elasticity
14(1)
BEM in Elasto-Plasticity
14(1)
Closure
15(1)
Theory of Elasticity
16(9)
Introduction
16(1)
Displacements
16(1)
Stresses
17(1)
Stress-Strain Relationships
18(1)
Navier--Cauchy Equations of Equilibrium
19(1)
Reduced Forms in Two Dimensions
20(3)
Plane Strain
21(1)
Plane Stress
22(1)
Axisymmetry
22(1)
Anisotropic Materials
23(1)
Closure
24(1)
Boundary Integral Equations for Elasticity
25(9)
Introduction
25(1)
The Kelvin Fundamental Solution
25(2)
Betti's Reciprocal Work Theorem
27(1)
Somigliana Identity
28(2)
Boundary Integral Equations
30(1)
Internal Stresses
31(2)
Closure
33(1)
Numerical Implementation
34(33)
Introduction
34(1)
Boundary Discretization
34(3)
Interpolation of Field Quantities
37(1)
Discretized Boundary Integral Equations
38(1)
Adaptive Integration
39(8)
Singular Integration
47(6)
Weakly Singular Integrals in Three Dimensions
47(2)
Weakly Singular Integrals in Two Dimensions
49(2)
Strongly Singular Integrals
51(2)
Evaluation of Boundary Stresses
53(4)
Symmetry
57(3)
Corners and Edges
60(3)
Multiple Regions
63(1)
System Equation Solution
64(2)
Closure
66(1)
The Elastic Program Code
67(40)
Introduction
67(1)
Scope of the Program
67(1)
Program Structure
67(1)
Global Variables
68(7)
Global Variables in Module Program Units
68(7)
Global Variables Passed through Argument Lists
75(1)
Main Program: BEMECH
75(1)
Subroutine INPUT-CTR
76(1)
Subroutine BLOCK-DATA
77(1)
Subroutine INPUT-EL
78(1)
Subroutine TREAT-T
79(1)
Subroutine AXES-COS
80(1)
Subroutine SHAPEF
81(1)
Subroutine DSHAPE and DSHAP3D
82(2)
Subroutine EL-COEFS
84(1)
Subroutine ADAPTINT
85(2)
Subroutine CHOSEGP
87(2)
Subroutines SETGAS and GAUSSV
89(1)
Subroutines MINDIST and IVSNR 123
90(1)
Subroutine INT-HG
91(1)
Subroutine EVAL-HG
92(1)
Subroutine FORM-HG
93(1)
Subroutine SINGUGH
94(1)
Subroutine SIN2DHG
95(1)
Subroutine SETDSUB
96(1)
Subroutine BDSTRS
97(1)
Subroutine BSCOEF
98(1)
Subroutine SYMTRY
99(1)
Subroutine HGTOEQS
100(1)
Subroutine INNERPS
101(1)
Subroutine EL-SOLVE
102(1)
Subroutine INVSOLVR
103(1)
Subroutines OUTPUT and SIGTITL
104(2)
Closure
106(1)
Linear Applications
107(14)
Introduction
107(1)
Thick-Walled Cylinder under Internal Pressure
107(4)
Circular Rigid Foundation on a Semi-Infinite Medium
111(1)
A Three-Dimensional Machine Component
112(5)
Closure
117(4)
PART II. NONLINEAR PROBLEMS
Rate-Independent Plasticity Theory
121(17)
Introduction
121(1)
Isotropic Yield Criteria
121(5)
Stress Invariants and Principal Stresses
122(1)
The Tresca Criterion
123(1)
The Von Mises Criterion
124(1)
The Mohr--Coulomb Criterion
124(1)
The Drucker--Prager Criterion
125(1)
Principles of Elasto--Plastic Flow
126(2)
Constitutive Relationships
128(2)
Isotropic Hardening Materials
130(4)
Equivalent Uniaxial Yield Criteria
131(1)
Equivalent Plastic Strain
131(1)
Explicit Derivations
132(2)
Kinematic Hardening Materials
134(1)
Mixed Hardening Materials
135(1)
Closure
136(2)
Boundary Integral Equations in Elasto-Plasticity
138(8)
Introduction
138(1)
Boundary Integral Equations
138(2)
Internal Stress Integral Equations
140(3)
Integration of Strongly Singular Domain Integrals
143(2)
Closure
145(1)
Numerical Implementation
146(16)
Introduction
146(1)
Domain Discretization
146(2)
Weakly Singular Domain Integrals
148(1)
Strongly Singular Domain Integrals
149(1)
Boundary Stresses - Traction-Recovery Method
150(3)
System Equations
153(3)
Initial Stress Representation
153(1)
Plastic Multiplier Representation
154(2)
System Equation Solution
156(4)
Newton-Raphson Method
156(1)
Transition from Elastic to Elasto-Plastic States
157(1)
Automatic Incrementation of Boundary Loading
158(1)
Summary
159(1)
Closure
160(2)
The Elasto-Plastic Program Code
162(25)
Introduction
162(1)
Scope of the Program
162(1)
Program Structure
162(2)
Global Variables
164(1)
Subroutine INPUT_NL
165(1)
Subroutine NL_COEFS
166(1)
Subroutine INT_CELL
167(1)
Subroutine SIN_CELL
168(2)
Subroutine CELL_BOUND
170(1)
Subroutine EVAL_KE
171(2)
Subroutine INTSUBC
173(1)
Subroutine PBSCOEF
173(1)
Subroutine NL_SOLVE
174(2)
Subroutine PL_FLOW
176(1)
Subroutine DF_DSIG
177(1)
Subroutine P_M_ITER
178(3)
Subroutine MATRICES
181(1)
Subroutine SIG_SCALE
182(1)
Subroutine SIGCROSS
183(1)
Subroutine DF_MATRX
184(1)
Subroutine UPDATEV
185(1)
Closure
186(1)
Nonlinear Applications
187(16)
Introduction
187(1)
A Cube Subjected to Uniaxial Tension
187(4)
A Thick-Walled Cylinder Subjected to Internal Pressure
191(2)
A Rigid Punch under Plane Strain
193(3)
A Flexible Square Footing
196(3)
Multiplanar Tubular DX-Joint
199(2)
Closure
201(2)
Epilogue
203(6)
Review
203(1)
The Way Forward
203(6)
Automatic Integration
203(1)
Computation of Boundary Stresses
204(1)
Stress-Return Algorithm
204(1)
System Equation Solver
205(1)
Local Boundary Conditions
205(1)
Nonlinear Hardening
206(1)
Advanced Yield Functions
206(1)
Finite Strain Elasto-Plasticity
206(1)
Infinite Boundary Elements
207(1)
Multiple Regions
207(2)
Appendix A. Derivation of Kernel Functions 209(4)
A.1. Derivation of the Strain Kernel
209(1)
A.2. Derivation of the Stress Kernel
210(1)
A.3. Derivation of the Traction Kernel
211(1)
A.4. Kernel Functions for Plane Strain and Plane Stress
211(2)
Appendix B. Shape Functions 213(4)
B.1. One-Dimensional Shape Functions
213(1)
B.2. Two-Dimensional Shape Functions
214(1)
B.3. Three-Dimensional Shape Functions
215(2)
Appendix C. Degenerate Elements: Singular Mapping 217(4)
Appendix D. Elasto-Plastic Flow Theory 221(7)
D.1. Derivation of the Plastic Flow Rule and Plastic Loading Rule
221(3)
D.2. Derivations for Kinematic Hardening Materials
224(1)
D.3. Derivations for Mixed Hardening Materials
225(1)
D.4. Derivation of the Deformation State Function Γ
226(2)
Appendix E. Domain Integral Formulations 228(4)
E.1. Boundary Integral Equations: Initial Strain Formulation
228(1)
E.2. Analytical Integration of the Strongly Singular Volume Integral
228(2)
E.3. Interior Stress Equation: Initial Strain Formulation
230(1)
E.4. Analytical Integration of Eijkl in Two Dimensions
230(1)
E.5. Analytical Integration: Initial Strain Formulation
231(1)
Appendix F. Solution of the Nonlinear System Equations 232(7)
F.1. The Newton-Raphson Iterative Algorithm
232(1)
F.2. System Equation Solution Strategies
233(6)
F.2.1. The Initial Stress Iteration Technique
234(1)
F.2.2. The Implicit Solution Technique
235(1)
F.2.3. The Variable Stiffness Technique
236(1)
F.2.4. The Mixed Representation Technique
237(2)
Appendix G. Elements of Elasto-Plasticity 239(3)
Appendix H. Description of Input Data 242(5)
References 247(6)
Index 253

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