The Boundary Element Method Applied to Inelastic Problems

1 Introduction and Motivation.- 1.1 Introduction.- 1.2 Literature Survey-Nonlinear Applications.- 1.3 Layout of Notes.- 2 Basic Theory.- 2.1 Introduction.- 2.2 Theory of Elasticity.- 2.3 Inelastic Behaviour of Materials.- 2.4 Governing Equations.- 3 Boundary Element Formulation for Elastic Problems.- 3.1 Introduction.- 3.2 Somigliana's Identity.- 3.3 Fundamental Solutions.- 3.4 Stresses at Internal Points.- 3.5 Boundary Integral Equation.- 3.6 Infinite and Semi-Infinite Regions.- 3.7 Numerical Implementation.- 3.8 Examples - Half-Plane Formulation.- 4 Boundary Element Equations for Inelastic Problems.- 4.1 Introduction.- 4.2 Somigliana's Identity for Inelastic Problems.- 4.3 Internal Stresses.- 4.4 Alternative Boundary Element Formulations.- 4.4.1 Initial Strain.- 4.4.2 Initial Stress.- 4.4.3 Fictitious Tractions and Body Forces.- 4.5 Half-Plane Formulations.- 4.6 Spatial Discretization.- 4.7 Internal Cells.- 5 Elastoplastic Boundary Element Analysis.- 5.1 Introduction.- 5.2 Some Simple Elastoplastic Relations.- 5.3 Initial Strain - Numerical Solution Technique.- 5.4 Examples - Initial Strain Formulation.- 5.4.1 Perforated Aluminium Strip.- 5.4.2 Polystyrene Crazing Problem.- 5.4.3 Plane Strain Punch.- 5.4.4 Thick Cylinder.- 5.5 General Elastoplastic Stress-Strain Relations.- 5.6 Initial Stress-Outline of Solution Techniques.- 5.7 Examples - Kelvin Implementation.- 5.7.1 Notched Tensile Specimen.- 5.7.2 Deep Circular Tunnel.- 5.7.3 Rough Punch.- 5.8 Examples - Half-Plane Implementation.- 5.8.1 Strip Footing.- 5.8.2 Shallow Tunnel.- 6 Viscoplasticity and Creep Using Boundary Elements.- 6.1 Introduction.- 6.2 Rate Dependent Constitutive Equations.- 6.3 Solution Technique.- 6.4 Examples.- 6.4.1 Deep Beam.- 6.4.2 Thin Disc.- 6.4.3 Plate Under Thermal Shrinkage.- 7 General Discussion and Conclusions.- References.- Appendix A Indirect Computation of Principal Values.- Appendix B Stress Rates at Boundary Nodes.- Appendix C Displacements Due to Constant Inelastic Strain Fields.- Appendix D Some Particular Expressions for 2-D Inelastic Problems.