Transient topology optimization for periodic thin-walled structures using material field series expansion method

Periodic thin-walled structures have been widely used in aerospace engineering due to their superior specific stiffness, specific strength, and excellent buckling resistance. Achieving optimal structural performance has become a paramount objective in contemporary structural design. While current research predominantly focuses on static optimization, practical engineering applications are often subject to dynamic loading conditions. This disparity underscores a critical gap between theoretical advancements and practical engineering requirements, necessitating dynamic optimization methodologies tailored to actual operational environments. In this paper, a transient topology optimization framework for periodic thin-walled structures is proposed to enhance the dynamic performance of periodic thin-walled structures. Representing the structural topology via material field series expansion (MFSE) enables both efficient parameterization of the design domain and smooth structural boundary descriptions, simultaneously reducing the number of design variables compared to conventional methods. On the micro-scale, the asymptotic homogenization method (AHM) is utilized to calculate the general stiffness coefficient of the element. On the macro-scale, the minimum time-domain average dynamic compliance is taken as the objective to drive the topology optimization on the micro-scale. Furthermore, the OSS10 algorithm is introduced to solve transient problems, achieving zero-order velocity response overshoot characteristics while maintaining second-order accuracy in both displacement and velocity computations. Numerical examples demonstrate the reliability and validity of the proposed method.