Topology optimization of aeronautical structures with stress constraints: general methodology and applications

Abstract

Structural optimization is a well known and frequently used discipline in aerospace applications since most of the optimization problems were stated in order to solve aeronautic structures. Since first works about structural topology optimization were published, different formulations have been proposed to obtain the most adequate design. Topology optimization of structures is the most recent branch of structural optimization. The first works about this topic were proposed by Bendsoe and Kikuchi in 1988 (Bendsoe, M. P. and Kikuchi, N. Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Engng., 1988, 71, 197–224). In this field of structural optimum design, the aim is to obtain the optimal material distribution of a given amount of material in a predefined domain. The most usual formulation tries to maximize the stiffness of the structure by using a given amount of material. In this paper, we present a minimum weight formulation with stress constraints that allows to avoid most of the drawbacks associated to maximum stiffness approaches. The proposed formulation is applied to the optimization of aeronautical structures. Some examples have been studied in order to validate the formulation proposed.