Topology Optimization of Truss Structures Considering Stress and Stability Constraints

Topology optimization is a free-form approach to designing efficient structural layouts. Although highlighted repeatedly in literature for its ability to identify creative, high performance designs, it is also well known that oversimplification of the underlying optimization formulation can lead to impractical structural solutions. A common truss optimization problem formulation is to minimize linear elastic strain energy for to a given structural mass (or minimize mass subject to a linear elastic deformation constraint). The optimal solutions obtained from such a formulation may often include thin members that cannot resist yielding or local buckling, and/or may include colinear members with unbraced hinges that destabilize the structure. Such solutions are, of course, impractical from structural engineering perspective. Incorporating stress and local (member) buckling constraints into the problem formulation to satisfy strength and stability requirements has been studied in literature and involves significant fundamental challenges. The authors review and discuss these challenges in this paper and extend an existing disaggregated formulation to include global (system) buckling constraints. The impact of each of these constraints on the optimized solution when applied independently as well as simultaneously is demonstrated for simple truss design problems. Although the algorithm is currently being scaled up to large design domains, the presented results clearly show that the incorporation of stress and local and global stability constraints results in more realistic design solutions.