The optimal structural design problem which we consider is the well-studied variable thickness sheet (VTS) problem. In this problem the structural stiffness is maximized with a constraint limiting the volume of the structure. The presentation shows that by using modern primal-dual interior point methods it is possible to solve large-scale VTS problems over 3D design domains using only a modest number of function evaluations. Our implementation does not require that the primal-dual saddle-point system is assembled or factorized. Instead, this is only involved in matrix-vector multiplications as part of Krylov subspace methods for computing the search direction in the interior point method. An extensive set of numerical experiments on 3D design domains suggest that the combination of techniques result in a robust and efficient method capable of solving large-scale instances of the VTS problem.

Keywords: Structural optimization, PDE constrained optimization, interior point methods, Krylov subspace methods, preconditioners