Topology optimization of Double-Double (DD) composite laminates considering stress control

Abstract

Double–double (DD) laminates are a new type of composite layups, which can achieve different structural properties by adjusting two sets of balanced fiber orientations. The combination of topology optimization and DD laminates can further enhance the advantages of composite materials as lightweight designs. Currently, most topology optimizations use compliance as the target. Existing optimization studies implementing stress control are mostly for isotropic materials. It is a great challenge to implement stress control during topology optimization of composite laminates, because the layer-wisely distributed stress brings a lot of design constraints and leads to many local optima. In this paper, we propose a nested p-norm method that integrates the Tsai–Hill failure criterion indexes of different elements in different layers into one design response, thus realizing the effective stress control for topology optimization of laminated structures. There are two levels of p-norm nested in the process: the inner p-norm approximates the maximum failure index of all the layers for one element, and the outer p-norm approximates the maximum failure index for all elements. The nested p-norm scheme is implemented under the framework of the Solid Isotropic Material with Penalization (SIMP) model, which is extended to DD laminates by interpolating the stiffness matrix of composites. Then, the optimization model is established by minimizing the maximum Tsai–Hill failure index using the function formulated by the proposed nested p-norm method under the constraint of the structural volume fraction and compliance. Next, stress sensitivities are calculated using the adjoint method. It is noticeable that the sensitivity with respect to the filtered projection density is separately calculated to improve the computational efficiency. Finally, typical examples of topology optimization with stress singularity such as an L-shaped bracket, a crack problem, a corbel structure, and an antenna support bracket are given. It is validated that the proposed nested p-norm method can effectively and efficiently reduce the stress concentration of laminate structures compared with the methods using single p-norm and layer-wise p-norm. Additionally, the optimization results show that the DD laminate has similar optimized configurations and optimization effects as those of the conventional Quad laminate with the equivalent stiffness.