Optimization strategies for discrete multi‐material stiffness optimization

Design of composite laminated lay‐ups are formulated as discrete multi‐material selection problems. The design problem can be modeled as a non‐convex mixed‐integer optimization problem. Such problems are in general only solvable to global optimality for small to moderate sized problems. To attack larger problem instances we formulate convex and non‐convex continuous relaxations which can be solved using gradient based optimization algorithms. The convex relaxation yields a lower bound on the attainable performance. The optimal solution to the convex relaxation is used as a starting guess in a continuation approach where the convex relaxation is changed to a non‐convex relaxation by introduction of a quadratic penalty constraint whereby intermediate‐valued designs are prevented. The minimum compliance, mass constrained multiple load case problem is formulated and solved for a number of examples which numerically confirm the sought properties of the new scheme in terms of convergence to a discrete solution.