Truss geometry and topology optimization with global stability constraints

In this paper, we introduce geometry optimization into an existing topology optimization workflow for truss structures with global stability constraints, assuming a linear buckling analysis. The design variables are the crosssectional areas of the bars, and the coordinates of the joints. This makes the optimization problem formulations highly nonlinear and yields nonconvex semidefinite programming problems, for which there are limited available numerical solvers compared with other classes of optimization
problems. We present problem instances of truss geometry and topology optimization with global stability constraints solved using a standard primal dual interior point implementation. During the solution process, both the the cross-sectional areas of the bars and the coordinates of thejoints are concurrently optimized. Additionally, we applyadaptive optimization techniques to allow the joints to
navigate larger move limits and to improve the quality of the optimal designs.