Topology optimization of fiber-reinforced materials for dynamic problems

In recent years, the popularity of fiber-reinforced materials in the aerospace and automobile industries grows due to their high stiffness-to-weight ratios. Thus, a structural design methodology is needed to bring out the celebrated mechanical properties of these materials as much as possible. From this aspect, topology optimization has been considered as an effective method for such a method. As a natural consequence of the trend, intensive researches on topology optimization methodologies to handle the anisotropy of fibrous materials has been conducted. However, these researches were limited to the static problem, i.e., compliance minimization problem. In the present work, we propose a dynamic topology optimization method for fiber-reinforced materials which is capable of optimizing element-by-element orientations. Our method builds upon a framework of SIMP type topology optimization and can optimize each element’s density and orientation as design variables. Numerical analysis is done by Finite Element Method and Method of Moving Asymptotes is implemented as an updating scheme of design variables. The effectiveness of our method is validated through the eigenfrequency maximization problem and eigenfrequency gap maximization problem.