Concurrent Topology and Stacking Sequence Optimization of Laminated Plates

Abstract

In the recent years there has been an increase on the development and application of additive manufacturing techniques permitting engineers to take advantage of non-traditional mechanical components designs. Among some techniques, topology optimization is an effective method to achieve additively manufactured layouts. Besides all the development of topology optimization procedures in recent years, most of the methods are dedicated to the solution of isotropic materials, leaving a gap in terms of the methodology applied to the optimization of composite plates. Composite materials provide an advantage when developing light-weight components because of their high strength to weight ratio and optimization potential. Nevertheless, unidirectional composite response is highly dependent on the laminate stacking sequence. Therefore, to take full advantage of the design freedom allowed by additive manufacturing new optimization solutions that can concurrently solve the shape and laminate orientation are essential for designing lightweight composite structures. Firstly, a new solution for the relation among the lamination parameters is proposed. A set of ten feasible region inequations that fully describe the relation among the in-plane and out-of-plane lamination parameters is presented. A three-step angle retrieval approach is also presented allowing the layup definition from the optimum lamination parameters. These methods are applied on the concurrent topology and stacking sequence optimization. Secondly, the problem is expanded to the application of angle minus longitudinal theory, where only plies at 0º, ±45º and 90º are considered. A new approach to retrieve the stacking sequence is discussed and applied to the simultaneous topology and stacking sequence optimization for frequency response optimization. Thirdly, a novel approach to compute the sensitivities for the isotropic and anisotropic materials mixture is presented. The proposed method improves the numerical efficiency of the multimaterial topology optimization compared with element duplication methods as well as being an alternative to compute the sensitivities in the discrete material optimization scheme. Finally, a solution for the multi-material topology optimization considering the stacking sequence of the laminated plates is discussed. The methods presented in the previous chapters are integrated in a framework that optimizes for the material selection, placement and stacking sequence for a non-discrete composite material candidate.