A. Weldeyesus, J. Gondzio, Linwei He, M. Gilbert, P. Shepherd, A. Tyas
In this paper, we introduce geometry optimization into existing topology optimization of truss structures with global stability constraints. The design variables are the cross-sectional areas of the bars, and the coordinates of the joints. This makes the optimization problem formulations highly nonlinear and yields nonconvex semidefinite programing problems, for which, there are only limited available solvers when compared to that of other classes of optimization problems. In this study, we present problem instances of truss geometry and topology optimization with global stability constraints that have been 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 the joints are concurrently optimized. Additionally, we apply adaptive optimization techniques to allow the joints to navigate larger move limits and improve the quality of the optimal designs.
Key words: Geometry and topology optimization, Global stability, Semidefinite programming, Interior point methods.