Structural Shape Optimisation Using Boundary Elements And The Biological Growth Method.

Abstract

A numerical evolutionary procedure for the structural optimisation for stress
reduction of two-dimensional structures is presented in this paper. The proposed procedure
couples the Biological Growth Method (BGM) with the Boundary Element Method (BEM).
The boundary-only intrinsic characteristic of BEM together with its accuracy in the boundary
displacement and stress solutions, make boundary elements especially attractive for solving
shape optimisation problems. Two formulations of BEM are used in this work: the standard
for two-dimensional elastostatics for the stress analysis, and the Dual Reciprocity Method
(DRM) which is used to model the swelling or shrinking of the material. Two examples are
analysed to illustrate the proposed methodology and to demonstrate its versatility and
robustness.