On the application of the boundary element method to inelastic problems

Faria Telles, José Claudio de (1981) On the application of the boundary element method to inelastic problems. University of Southampton, Doctoral Thesis.

Abstract

The object of this work is the application of the direct boundary element method for the solution of nonlinear material problems. To this end, the elastic formulation of the technique is first introduced by considering two and three dimensional problems employing the fundamental solutions corresponding to the infinite and semi-infinite spaces. Thus, in addition to the known Kelvin and Mindlin solutions, the complete fundamental solution due to a unit point load within the half-plane is presented and its implementation discussed in detail, including the results of some classical examples.Three alternative formulations - initial strain, initial stress and fictitious forces - are discussed for 3-D and 2-D inelastic problems. The numerical implementation of the first two approaches is then presented for two dimensional problems, including the half-plane fundamental solution. The problem of accurately integrating the inelastic contribution within the domain is overcome by employing a semi-analytical integration scheme, which is also applied to computing principal values. This integration scheme has proved to be efficient for the case of triangular cells with linear interpolation functions. However, for general purposes, an indirect, procedure for computing such principal values is also proposed. Different applications of the inelastic boundary element equations to pure elastoplastic analysis are presented. The initial strain, formulation is implemented with the von Mists yield criterion and employs a simple solution technique. The initial stress implementation is more general and can handle four different yield criteria, with two different solution routines. A common feature of the alternative implementations is that they are all incremental - iterative processes, capable of performing iterations by using a single recursive expression, relating stresses to the plastic strains and the initial elastic solution. Finally, the implementation of the BE technique to viscoplasticity and creep is accomplished by using the initial stress equations in conjunction with an Euler time integration procedure.Several examples are presented to outline the accuracy and applicability of the different formulations, these involve elastoplastic, creep and viscoplastic problems.

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