3D non-linear and multi-region boundary element stress analysis
The new findings can be outlined as follows: Two new simple auxiliary equations which are required to supplement the fundamental boundary integral equations in solving traction-discontinuity problems using multiple-node technique are derived from the symmetric property and the equilibrium equations of the stress tensor. These equations have been used to deal with the corners and edges of single region and multi-region problems. A sub-structure algorithm is developed for solving multi-region problems with corners and edges, using the derived auxiliary equations. This algorithm can deal with nodes where more than two materials intersect. A novel infinite element formulation suitable for multi-layered media was developed. In particular, a set of useful analytical expressions was derived for evaluating strongly singular surface integrals over the infinite surface. A set of unified elastoplastic constitutive relationships dealing with hardening, softening and ideal plasticity behaviour is derived from the Il'iushin postulate in strain space. These relationships are suitable for both small and finite deformation rate-independent elastoplastic problems. Some new identities are derived for the initial stress and strain kernels. Based on these, a new transformation technique from domain integrals to cell boundary integrals is developed, for accurate evaluation of the strongly singular domain integrals pertaining to interior stresses. Two new iterative schemes are introduced for the first time in the incremental variable stiffness method for solving the non-linear system of equations. In particular, in the second one, a novel assembly process was proposed, in which the system equations are expressed in terms of the plastic multiplier. These formulations have been implemented within a Fortran computer code and illustrative numerical examples have been solved to demonstrate its practical utility.