A streamlined approximation and duality scheme for structural optimization

Abstract

An efficient and commonly used approach to structural optimization is to solve a sequence of approximate design problems that are constructed iteratively. As is well-known, a major part of the computational burden of this scheme lies in the sensitivity analysis needed to state the approximate problems. We propose a possibility for reducing this burden by streamlining the calculations in a combined approximation and duality scheme for structural optimization. The difference between this scheme and the traditional one is that, instead of calculating all the constraint gradients to state an approximate design problem explicitly, linear combinations of these gradients are generated as they are needed during the solution of the approximate problem by the dual method. We show, by analysing some typical scenarios of problem characteristics, that this rearrangement of the calculations may be a computationally viable alternative to the traditional scheme. An advantage of streamlining the calculations is that there is no need to incorporate an active set strategy in the scheme, as is usually done, since all the design constraints may be taken into consideration without any loss of computational efficiency. This may, clearly, enhance the practical rate of convergence of the overall approximation scheme. Moreover, the proposed rearrangement of the calculations may make it computationally viable to apply iterative equation solvers to the structural analysis problem. Numerical results with direct as well as iterative equation solvers show that the streamlined scheme is a feasible and promising approach to structural optimization.