The coupling of the FEM and the BEM for the solution of elastoplacticity and contact problems

Abstract

This thesis introduces a method for the coupling of the elastic Boundary Element Method (BEM) and the elastoplastic Finite Element Method (FEM) and the extension of this method to contact problems by using gap finite elements. A method for the coupling of BEM subregions and FEM subregions is derived which limits the transformation of nodal forces into nodal traction to the interface degrees of freedom. This method is also capable of modelling body forces. Then the coupling procedure is extended to allow for elastoplastic material models in the FEM parts of the structure. Additionally contact conditions are included by defining an extra artificial subregion which consists of gap finite elements. Incremental iterative algorithms are used to overcome the present nonlinearities resulting from plasticity, non-conforming contact and friction. A computer program based on the developed methods and algorithms was coded in FORTRAN77 and tested on PCs. Patch tests and case studies were run in order to validate the developed package against known analytical solutions or the commercial finite element package ABAQUS. It can be concluded that all the original ideas and methods developed in this work are successful. The coupled FEM/BEM is as accurate and reliable as the pure FEM for elastoplastic analysis, with FEM/BEM having the advantage of ininimising the modelling effort. The use of gap elements in an artificial subregion was found to be an ideal and accurate way of including contact conditions into the environment of the elastoplastic coupled FEM/BEM.