GLOBAL TOPOLOGY STIFFNESS OPTIMIZATION OF FRAME STRUCTURES BY MOMENT-SUM-OF-SQUARES HIERARCHY

Abstract

: This contribution develops an efficient formulation for the topology optimization of frame structures with fixed-aspect-ratio cross-sections, solvable to global optimality by the moment-sum-of-squares hierarchy. While the hierarchy generates a sequence of non-decreasing lower-bounds, we develop a sequence of feasible upper-bounds, allowing to assess the optimized design quality in each relaxation. Finally, these bounds provide a means of establishing a new sufficiency condition of global ε-optimality.