On globally stable singular truss topologies

Abstract

We consider truss topology optimization problems including a global stability constraint, which guarantees a sufficient elastic stability of the optimal structures. The resulting problem is a nonconvex semi-definite program, for which nonconvex interior point methods are known to show the best performance. We demonstrate that in the framework of topology optimization, the global stability constraint may behave similarly to stress constraints, that is, that some globally optimal solutions are singular and cannot be approximated from the interior of the design domain. This behaviour, which may be called a global stability singularity phenomenon, prevents convergence of interior point methods towards globally optimal solutions. We propose a simple perturbation strategy, which restores the regularity of the design domain. Further, to each perturbed problem interior point methods can be applied.