Concurrent topology optimization design for CNT orientation and CNTRC layout

Abstract

In this study, the topology optimization (TO) design of carbon nanotube (CNT) orientation and material layout for carbon nanotube-reinforced composites (CNTRCs) is performed for the first time. The equivalent performance of CNTRCs is calculated by the extended easy-to-implement rule of mixtures. Then, by considering two independent angle variables, a 3-dimensional (3D) concurrent optimization model for CNT orientation and material layout is constructed. To decrease the possibility of falling into local optimal solutions, a discrete interval method is proposed to divide the search space into specific subintervals, and thus the original optimization problem is changed into material selection and subinterval angle optimization problems. In addition, different from conventional fiber-reinforced composites, CNTRCs employ nanoscale filler as reinforcement, which makes it more beneficial to achieve local material strengthening. Therefore, to decrease the possibility of local optimal solutions and achieve local structural strengthening, a concurrent TO model involving CNTRCs and isotropic materials under the volume constraint is proposed to achieve the optimal balance between structural stiffness and economy. Subsequently, the sensitivities of structural compliance with respect to design, selection, and angle variables are derived. Also, the effectiveness of the proposed method is verified by 2D and 3D examples.