Abstract:

Compared with traditional metal-materials, fiber-reinforced composite materials have better performance in many aspects such as strength, stiffness, and fracture resistance. At present, fiber-reinforced composite materials have been widely used in automotive, aerospace, and other industrial fields. This paper proposes a topology optimization method for solving the fundamental frequency maximization of undamped free vibration of continuous fiber-reinforced composite structures. To achieve the simultaneous optimization of the structural topological configuration and the fiber angle. A dynamic topological optimization model is established with the permitted material usage as the constraint and the structure's first-order eigenvalue as the objective function. The model includes density design variables that characterizes the topological configuration of the structure and angular design variables that characterizes the fiber orientation. The analytical sensitivity formulas of the objective function of eigenvalue with respect to density design variables and angle design variables are derived in detail, and the method of moving asymptotes (MMA) is used to solve the optimization problem. Finally, three numerical examples are performed to verify the effectiveness of the proposed method, which includes a static optimization example with the stiffness maximization as the goal and two dynamic optimization examples with the first-order eigenvalue maximization as the goal. The results show that the proposed method can achieve a stable iterative history and fast convergence, and can effectively improve the structural frequency while achieving the integrated optimization of the structural topological configuration and the fiber angle.

Key words: topology optimization, continuous fiber, dynamic optimization, SIMP method