A simple QP modification of the OC update to permit treatment of the topology design problem of self-weight

Abstract

This note communicates a simple modification of the optimality criteria (OC) design update—as found in well-known Matlab implementations of the classical topology design problem—to an update based on a quadratic program (QP) with a single linear constraint. This QP update is a special case of the dual of Falk, which in general accommodates multiple constraints, as discussed in the Appendix. It is demonstrated that the topology design problem of self-weight may be treated with judicious selection of the adaptive curvature term in the QP, without resorting to more sophisticated algorithms or material interpolation schemes. Theory is recited and an accordingly modified version of the canonical Matlab implementation is provided as supplementary material.