Combining topology and lamination parameter optimisation

Two dimensional composite structures are designed for maximum stiffness under multiple load cases. Both the topology and the fibre angle distribution are optimised simultaneous. To solve the topology optimisation, a density approach is used. The stiffness is parametrised in terms of lamination parameters, not directly in terms of the fibre angles. To force the fictitious density to either zero or one both implicit and explicit penalisation are used. Both penalisation approaches are implemented and both give a satisfactory result. Once the optimum lamination parameter and density distribution is found, some post-processing steps are necessary: the boundaries of the structure are determined by post-processing the density distribution. The fibre angle distribution is found by matching the lamination parameter distribution. Finally the fibre paths are determined. A number of examples are worked out to demonstrate the technique for balanced, unbalanced, single and multiple load case problems. The results show that the proposed technique is widely applicable and that there are considerable benefits in exten ding topology optimisation to handle composites.