1 Applied functional analysis, Department of Mathematics, Technical University of Denmark2 Department of Mathematics, Technical University of Denmark3 Department of Wind Energy, Technical University of Denmark4 Department of Applied Mathematics and Computer Science, Technical University of Denmark5 University of Birmingham
The multiple load structural topology design problem is modeled as a minimization of the weight of the structure subject to equilibrium constraints and restrictions on the local stresses and nodal displacements. The problem involves a large number of discrete design variables and is modeled as a non-convex mixed 0–1 program. For this problem, several convex and mildly non-convex continuous relaxations are presented. Reformulations of these relaxations, obtained by using duality results from semi-definite and second order cone programming, are also presented. The reformulated problems are suitable for implementation in a nonlinear branch and bound framework for solving the considered class of problems to global optimality.
Topology optimization; Stress constraints; Relaxations; Global optimization