Topology optimization method for continuous fiber reinforced composites with different moduli in tension and compression

Continuous fiber -reinforced composite (CFRC) materials may exhibit different moduli in tension and compression. This nonlinear behavior significantly impacts the optimal design of CFRC structures. However, current topology optimization methods for CFRCs primarily rely on the assumption of uniform moduli, leading to inaccurate analyzes and suboptimal results. In this paper, a novel concurrent topology, fiber orientation and fiber content optimization method for CFRCs is proposed with the property of different moduli in tension and compression being considered. The tension/compression bi-modulus orthotropic property is incorporated through the weighted compliance matrix (WCM) material model. To solve the nonlinear equilibrium equation, a computational framework based on the Newton-Raphson method is established and the accurate tangent stiffness matrix is derived. The macro topology and fiber content distribution are optimized utilizing the density -based topology optimization method. Concurrently, elementwise fiber orientations are optimized by determining the rotation angles of the material orthotropy. The three design variables, namely macro topology, fiber content distribution, and fiber orientations, are all updated using the method of moving asymptotes (MMA) while calculating the sensitivities of the objective. In the numerical examples, various tension/compression modulus ratios are employed to explore the impact of modulus asymmetry on the optimized results and to demonstrate the effectiveness of the proposed method. The convergence of the computational framework is verified by extracting equilibrium errors during the iterations. Furthermore, the paper presents several extensions of the method, including dealing with problems involving multiple loads and multiple bi-modulus orthotropic materials. A distinct constitutive model is also used to establish the optimization method for the bi-modulus orthotropic materials for verification as shown in Appendix B.