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Fiber-reinforced composites are currently considered engaging materials by engineers and researchers in automobile, aerospace, robotics, and other related industries and scholars in academics due to their superior mechanical properties.Using the materials as structural materials allows engineers to make lightweight but high-stiff mechanical structures happen in reality. By adopting a structural optimization methodology, they can explore further and bring out the mechanical properties of composites as much as possible to design innovative composites structures. Based on this background, it has already been a hot research topic to establish a method for concurrent optimization of topology and fiber orientation in the structural optimization research field. This optimization method will be more effective in the real world by considering uncertainties that engineers commonly encounter. However, anisotropic topology optimization researches on this motivation are very rare. In the present work, we propose a robust topology and orientation optimization methodology accounting for fiber manufacturing uncertainty, namely orientation uncertainty. The proposed method is built upon the Phase Field and the Method of Moving Asymptotes based SIMP type topology optimization and EOLE-PCE uncertainty quantification. Numerical analysis is done by the Finite Element Method. The effectiveness of the proposed method is validated through the compliance minimization problem and the fundamental eigenfrequency maximization problem.

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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.

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