A modified topological sensitivity analysis extended to the design of composite multidirectional laminates structures

The main purpose of this study is to analyze two main problems, namely the optimal design of multilayered composite laminates and the topological sensitivity analysis in anisotropic elastostatics. Regarding the composite design, minimal weight structures subjected to bending and Hoffmann failure criteria constraints are considered, where the design variables are the shape/topology of each ply and the stacking sequence. The application of topological sensitivity analysis is extended to obtain the optimal topology of composite laminated structures. From the topological Derivative mapping methodology, considering the total potential energy as an objective function, the optimal topology is obtained by gradual insertion of material in the considered domain. The Topological Derivative defines the shape of the new added plies, and the optimal layup is obtained by using an ant colony optimization algorithm. Numerical examples are presented to demonstrate the validity, functionality and applicability of the proposed methods.