Simultaneous Optimization of Truss Topology and Geometry, Revisited

The paper considers the problem of simultaneous truss geometry and topology optimization. We tackle the classical problem of minimal compliance subject to a volume constraint which alternatively can be regarded as a minimum volume problem subject to symmetric stress constraints. After the review of a bilevel approach of Kocvara et al. we propose three closely related approaches which, however, overcome the pitfall of vanishing potential bars for melting end nodes. This is achieved through the use of the data structure of the problem allowing a split of the dependence of the data on the geometry variable into a linear and a quadratic part. The paper closes with some numerical experiments based on the new problem formulations. In particular, we are interested in a relation of the number of potential bars needed in a pure topology approach and a simultaneous geo/topo approach, respectively, to achieve the same value of optimal compliance resp. volume.