Load sensitivity analyses of elastic structures by differential and boundary integral equation formulations

Abstract

A direct unification of the boundary integral equations (BIE) of elasticity and load sensitivity analysis procedures is proposed in a novel approach. In the so-called BIE formulation, it is found that more than one type of adjoint functions are necessary, which are defined by different integral equations at complementary points of the structural boundary. The presence of double volume/surface integrals and the switching of the source and field points in the fundamental solutions are further interesting characteristics of the proposed formulation. An analytical example is solved by using the standard differential equation formulation, as well as the new BIE formulation of load sensitivity analysis.

Engineering optimization with the fast boundary element method

“…A number of efficient shape optimization techniques have been developed subsequently, including boundary variation algorithms [2], level set methods [3], homogenization [4]. A number of works illustrated that boundary variation optimization approaches are naturally treated with boundary element method (BEM) [5]. Few recent works [6,7] have also demonstrated that BEM can be a convenient tool for topological-shape optimization.…”