A. Weldeyesus, J. Gondzio, Linwei He, M. Gilbert, P. Shepherd, A. Tyas
Abstract
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.