Topology optimization of structures with stress constraints: Aeronautical applications

Topology optimization of structures is nowadays the most active and widely studied branch in structural optimization. This paper develops a minimum weight formulation for the topology optimization of continuum structures. This approach also includes stress constraints and addresses important topics like the efficient treatment of a large number of stress constraints, the approach of discrete solutions by using continuum design variables and the computational cost. The proposed formulation means an alternative to maximum stiffness formulations and offers additional advantages. The minimum weight formulation proposed is based on the minimization of the weight of the structure. In addition, stress constraints are included in order to guarantee the feasibility of the final solution obtained. The objective function proposed has been designed to force the convergence to a discrete solution in the final stages of the optimization process. Thus, near discrete solutions are obtained by using continuum design variables. The robustness and reliability of the proposed formulation are verified by solving application examples related to aeronautical industry.