Concurrent topology and geometry optimization of truss structures with global stability constraints

Several models of truss topology and geometry optimization have been proposed and extensively studied. In this paper, we extend the formulations to take into account global stability constraints via semidefinite programming, for which we have also implemented a solution technique based on a second-order interior point method. The optimal designs obtained by solving geometry optimization are known to depend hugely on the initial configuration of the joints due to the associated restrictive move limits to avoid computational instabilities. In order to minimize this dependency, we have employed an adaptive procedure where the problems are initially solved by restricting the movement of the joints to smaller regions, and then progressively updating these. We demonstrate the approach benefits the joints to navigate much larger regions in the design domain, and results in a significant reduction of the weight of the obtained optimal designs. We perform several numerical experiments to validate the proposed model, the implemented optimization method, and the adaptive procedure.