A STREAMLINED APPROXIMATION AND DUALITY SCHEME FOR STRUCTURAL OPTIMIZATION

An efficient and commonly used approach to structural optimization is to solve a sequence of approximate design problems that are constructe d iteratively. As is well-known, a major part of the computational bur den of this scheme lies in the sensitivity analysis needed to state th e approximate problems. We propose a possibility for reducing this bur den by streamlining the calculations in a combined approximation and d uality scheme for structural optimization. The difference between this scheme and the traditional one is that, instead of calculating all th e constraint gradients to state an approximate design problem explicit ly, linear combinations of these gradients are generated as they are n eeded during the solution of the approximate problem by the dual metho d. We show, by analysing some typical scenarios of problem characteris tics, that this rearrangement of the calculations may be a computation ally viable alternative to the traditional scheme. An advantage of str eamlining the calculations is that there is no need to incorporate an active set strategy in the scheme, as is usually done, since all the d esign constraints may be taken into consideration without any loss of computational efficiency. This may, clearly, enhance the practical rat e of convergence of the overall approximation scheme. Moreover, the pr oposed rearrangement of the calculations may make it computationally v iable to apply iterative equation solvers to the structural analysis p roblem. Numerical results with direct as well as iterative equation so lvers show that the streamlined scheme is a feasible and promising app roach to structural optimization.