Topology optimization considering static failure of composite laminate with the layerwise theory

Abstract

As the static safety of a mechanical structure is an important factor in engineering design, the consideration of the static failure of a structure has become an important topic in topology optimization (TO). Some difficult issues in considering static failure are solved with the help of some recent relevant researches. However, this research found that the singularity issue, which refers to the difficulty in obtaining the global optima with the KKT condition, is not serious and can be mathematically relaxed for reinforcement TO design. Moreover, it was found that the existing qp-relaxation stress interpolation scheme to resolve the singularity issue in TO shows the local optima issue in the reinforcement TO design with different penalization factors in solid isotropic material with penalization (SIMP). In order to explain this feature, the TO problems in simple benchmark truss structures are revisited. Several two-dimensional examples with in-plane load are solved to confirm the validity of the present study. Furthermore, in this thesis, we developed a topology optimization method by considering the failure of composite laminates with the layerwise theory. Most of the topology optimization methods developed for composite laminates use the classical plate theory to analyze composite laminates. However, in this thesis, we applied the layerwise theory to the analysis process to improve the accuracy and efficiency. Therefore, a new stress-based topology optimization method with newly defined displacement formulation and finite element models in the layerwise theory has been developed. In addition, each layer of a composite laminate composed of several layers is rotatable and causes a difference in the mechanical properties due to rotation. Because this rotation affects the optimal shape, an attempt has been made to find the optimum angle to maximize the stiffness of the structure. To set the constraint on the stress of the composite laminate, it is necessary to choose whether to consider the entire layer or a specific layer. In this thesis, a method is developed for calculating the global stress to be set as the constraint according to the selection. The performance and effects of the developed global stress calculation method can be verified by solving several numerical examples.