A Second Generation Structural Shape Optimization Capability Employing a Boundary Element Formulation

Abstract

References (1–3) describe a novel analytical formulation of numerical techniques and their implementation in a computer program to perform shape optimization research. This work involved coupling a boundary element fomulation for structural analysis and design sensitivity analysis with geometry, meshing, numerical optimization, and computer graphics. This paper describes research efforts to greatly enhance this technique including boundary element substructuring (matrix condensation) re-analysis techniques, and matrix sparsity exploitation. Implicit differentiation of the discretized boundary integral equations has been shown to produce a computationally efficient, accurate, and general form of design sensitivity analysis. In this paper it is shown that a form of boundary element substructuring (matrix condensation) can be utilized to form a dramatically economized “reduced problem.” Expressions for the efficient calculation of required reduced matrix sensitivities are also given. Re-analysis strategies are presented that re-use unchanging portions of matrix triangular factorizations during the optimization process.