Book:S.L. Crouch/Boundary Element Methods in Solid Mechanics

S.L. Crouch and A.M. Starfield: Boundary Element Methods in Solid Mechanics

Published $\text {1983}$, Unwin/Hyman

ISBN 0-04-445913-0

Subject Matter

• Applied Mathematics

Contents

Preface

List of tables

1 Introduction

2 Review of linear elasticity

2.1 Introduction

2.2 Stress

2.3 Strain

2.4 Generalized Hooke's Law

2.5 Index notation

2.6 Plane stress and plane strain

2.7 Formulation of elasticity problems

2.8 Co-ordinate transformations

3 Introduction to boundary element methods

3.1 Normal load on a half-plane (Flamant's problem)

3.2 Distributed loading

3.3 An indentation problem

3.4 Numerical procedure

3.5 Solution of rigid die problem

3.6 Non-uniform element spacing

3.7 Incorporation of symmetry condition

3.8 Recapitulation

3.9 Integral formulation

4 The fictitious stress method

4.1 Introduction

4.2 Kelvin's problem for plane strain

4.3 Constant tractions over a line segment

4.4 Numerical procedure

4.5 Co-ordinate transformations

4.6 Influence coefficients

4.7 Interior / exterior problems

4.8 Symmetry conditions

4.9 Examples

4.10 Program structure

5 The displacement continuity method

5.1 Introduction

5.2 Displacement discontinuity in an infinite solid

5.3 Pressurized crack problem

5.4 Numerical procedure

5.5 Co-ordinate transformations

5.6 Influence coefficients

5.7 Interior / exterior

5.8 Symmetry conditions

5.9 Examples

5.10 Computation of tangential stress along a boundary

6 The direct boundary integral method

6.1 Introduction

6.2 The reciprocal theorem and its consequences

6.3 Selection of the test solutions

6.4 Influence conditions

6.5 Formulation of the system of equations

6.6 Example

6.7 Somigliana's formlas

6.8 Co-ordinate transformations

6.9 Another formulation of the method

7 Improvements and extensions

7.1 Introduction

7.2 A higher-order formulation of the direct boundary integral method

7.3 Crack tip elements

7.4 Program modules for a half-plane

7.5 Inhomogeneous bodies

7.6 Program modules for bonded half-planes

7.7 Anisotropic elasticity

8 Applications in rock mechanics and geological engineering

8.1 Numerical modeling in rock mechanics

8.2 Stresses and displacements around underground excavations in jointed rock

8.3 Excavations in stratified rock

8.4 Joints with cohesion and friction

8.5 Excavations in seam-type ore deposits

8.6 Simulation of mining in faulted rock

8.7 Tabular ore bodies; three-dimensional effects

Appendix A Computer program for the two-dimensional fictitious stress method (TWOFS)

Appendix B Computer program for the two-dimensional displacement discontinuity method (TWODD)

Appendix C Computer program for the two-dimensional direct boundary integral method (TWOBI)

References

Index

List of Tables

4.1 Stresses along $x$ axis of disk (TWOFS)

4.2 Radial and tangential displacements at boundary of hole (TWOFS)

5.1 Stresses along $x$ axis of disk (TWODD)

5.2 Radial and tangential displacements at boundary of hole (TWODD)

5.3 Displacements along right half of upper crack (see Fig. 5.11)

6.1 Radial and tangential displacements at boundary of hole (TWOBI)

7.1 Displacement discontinuity $\hat u_y \left({a}\right)$ at the center $x = a$ of an element at a crack tip