This paper incorporates hyperelastic materials, nonlinear kinematics, and preloads in eigenfrequency constrained density–based topology optimization. The formulation allows for initial finite deformations and subsequent small harmonic oscillations. The optimization problem is solved by the method of moving asymptotes, and the gradients are calculated using the adjoint method. Both simple and degenerate eigenfrequencies are considered in the sensitivity analysis. A well-posed topology optimization problem is formulated by filtering the volume fraction field. Numerical issues associated with excessive distortion and spurious eigenmodes in void regions are reduced by removing low volume fraction elements. The optimization objective is to maximize stiffness subject to a lower bound on the fundamental eigenfrequency. Numerical examples show that the eigenfrequencies drastically change with the load magnitude, and that the optimization is able to produce designs with the desired fundamental eigenfrequency.

本文在基于固有频率约束密度的拓扑优化中结合了超弹性材料，非线性运动学和预紧力。该公式允许初始有限变形和随后的小谐波振荡。通过移动渐近线的方法解决了优化问题，并使用伴随法计算了梯度。灵敏度分析中考虑了简单和简并的本征频率。通过对体积分数字段进行过滤，提出了一个恰当的拓扑优化问题。通过去除低体积分数元素，可以减少与无效区域中过度失真和伪本征模相关的数值问题。优化目标是在基本特征频率的下限范围内最大化刚度。