Lower bounding problems for stress constrained discrete structural topology optimization problems

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.

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