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.
Keywords: truss optimization, geometry optimization, bilevel programming