考虑瞬态响应的薄板结构阻尼材料层拓扑优化

讨论了敷设阻尼材料的薄板结构考虑瞬态响应时阻尼材料层的最优布局问题。基于SIMP方法构造人工阻尼材料惩罚模型和结构拓扑优化模型,以阻尼材料的相对密度作为设计变量,在给定阻尼材料用量的条件下,最小化结构瞬态位移响应的时间积分。由于结构整体呈现非比例阻尼特性,采用逐步积分法对结构的振动方程进行求解。通过伴随变量法得到目标函数对设计变量的灵敏度表达式,在此基础上采用基于梯度的移动渐近线方法求解。数值算例验证了优化模型与算法的合理性和有效性。

TOPOLOGY OPTIMIZATION OF DAMPING LAYER IN THIN-PLATE STRUCTURES CONSIDERING TRANSIENT RESPONSE

This paper investigates the optimal distribution of damping material in thin-plate structures considering transient response by using structural topology optimization method. Therein, an artificial damping penalty model similar to the SIMP model is adopted. In the topology optimization model, the relative densities of the damping material are taken as design variables and the volume constraint of damping material is considered. The design objective is to minimize the time integration of the structural transient response at specified positions. Since the structure exhibits a non-proportional damping effect, the vibration equations of the structure are solved by the time integration method. The design sensitivities of the vibrating structure under applied loads are calculated using the adjoint variable method. Then the topology optimization problem is solved with the method of moving asymptote algorithm, which is a gradient-based method. Numerical examples are presented for demonstrating the validity and effectiveness of the proposed optimization model and numerical techniques.