This study proposes a topology optimization method for dynamic problems based on the finite deformation theory to derive a structure that can reduce deformations for arbitrary dynamic loads that have large deformations. To obtain a structure that can minimize deformations due to dynamic loading for the isotropic hyperelastic model, the square norm of dynamic compliance is set as the objective function. A sensitivity analysis method of the equation of motion, based on Newmark's $\mathrm{β}$ method for unknown displacements, is presented in the current study. The analysis is carried out by developing a general design sensitivity equation that can accurately account for the response of the structure to dynamic loading and simultaneously display a high affinity for the general constitutive law by using the adjoint variable method. The accuracy of the obtained sensitivity is verified by using the finite difference method as a benchmark. Numerical examples are then used to demonstrate the validity of the proposed method. The results show that the proposed method is able to derive optimization results according to the magnitude of the applied load.

中文翻译：

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基于有限变形理论的动力问题拓扑优化

本研究提出了一种基于有限变形理论的动力问题拓扑优化方法，以推导出一种结构，该结构可以减少具有大变形的任意动态载荷的变形。为了使各向同性超弹性模型的动态载荷引起的变形最小化，将动态柔量的平方范数设置为目标函数。基于Newmark的运动方程灵敏度分析方法$\beta$未知位移的方法，在当前的研究中提出。该分析是通过开发通用设计灵敏度方程来进行的，该方程可以准确地解释结构对动态载荷的响应，同时使用伴随变量方法显示出对通用本构律的高度亲和力。以有限差分法为基准，验证所得灵敏度的准确性。然后使用数值例子来证明所提出方法的有效性。结果表明，所提出的方法能够根据所施加载荷的大小推导出优化结果。