Discrete Material Optimization of Laminated Composites - SIMP vs. Global Optimization

Abstract

Design of laminated composites structures is becoming increasingly important as the use of composite materials steadily increases. This development is driven by the aerospace, automotive and wind turbine industries who need still lighter and stiffer/stronger structures. This presents a very challenging design task that calls upon structural optimization tools for providing basic design ideas. However, existing methods for handling laminated composites suffer from problems with local optima when optimizing the fiber orientation, which is the key to efficient design with laminated composites. To counter this problem Discrete Material Optimization (DMO) was suggested in [1] where an alternative parametrization of the optimization problem is used, inspired by the procedures in topology optimization. The idea is to discretize the problem by using only a limited number of pre-defined candidate fiber orientations, each described by a constitutive matrix, Ci. The optimization problem is then parameterized on the element level by expressing the constitutive matrix for lamina j as \( C_j = \sum _i x_{ij} C_i \) where \( \forall x_{ij} \in \left\{ {0,1} \right\} \) are the design variables for material i in lamina j. The objective of the optimization is then to choose one distinct material from the set of candidates, i.e. \( \sum _i x_{ij} = 1,\forall j \). The design variables, xij, may be associated with a specific lamina/element or a patch consisting of several laminae/elements, thereby significantly reducing the total number of design variables. The constitutive matrices,Ci, may represent any type of material, allowing for simultaneously optimization for fiber orientation and material choice.