Boundary Elements in Shape Optimal Design of Structures

Abstract

The shape optimal design of shafts and two-dimensional elastic structural components is formulated using boundary elements. The design objective is to maximize torsional rigidity of the shaft or to minimize compliance of the structure, subject to an area constraint. Also a model based on minimum area and stress constraints is developed, in which the real and adjoint structures are identical but have different loading conditions. All degrees of freedom of the models are at the boundary, and there is no need for calculating displacements and stresses in the domain. Formulations based on constant, linear and quadratic boundary elements are developed. A method for accurately calculating the stresses at the boundary is presented, which improves considerably the design sensitivity information. A technique for an automatic mesh refinement of the boundary element models is also developed. The corresponding nonlinear programming problems are solved by Pshenichny’s linearization method. The models are applied to shape optimal design of several shafts and elastic structural components. The advantages and disadvantages of the boundary element method over the finite element techniques for shape optimal design structures are discussed with reference to applications. A literature survey of the development of the boundary element method for shape optimal design is presented.