Elasto-plastic Matrix Displacement Analysis of Three-dimensional Continua

Abstract

The author presented in his recent main lecture to the Society, “The Computer Shapes the Theory”, a number of novel developments in the matrix displacement method. Since the publication of the lecture and discussion will inevitably be delayed and cannot but illustrate the application of the new ideas on a series of examples, he has been repeatedly urged to summarise some of the more important theoretical contributions in the form of Technical Notes. The first deals with the elasto-plastic analysis, in the presence of strain hardening, of arbitrary three-dimensional configurations. The reader is assumed to be familiar with the corresponding elastic analysis given in refs. 2 and 3, where the medium is represented by a suitable assembly of tetrahedra under constant stress and strain. The corresponding two-dimensional case is investigated on the basis of triangles. Arbitrary anisotropic behaviour and large displacements were also included in refs. 2 and 3.