多位移等式约束拓扑优化及在光电精密结构设计中的应用

为了满足光电精密跟踪设备中光学系统对支撑结构变形位移相等的设计要求,基于变密度法,以刚度极大为目标,同时以体积约束和位移等式约束作为约束条件,构建结构拓扑优化模型。位移等式约束通过增广拉格朗日乘子法引入原目标函数,在拉格朗日乘子的求解中,采用考虑具有真实物理意义的近似替代法而非传统的纯数学迭代逼近方法。在利用伴随方法得到增广目标函数敏度基础上,采用MMA优化算法,在满足体积约束的同时进行迭代优化得到新结构。算例验证结果表明,本文方法能够有效解决具有多个位移等式约束的刚度极大结构轻量化设计问题。

Topology optimization with multiple displacement equality constraints and application in optoelectronic fine structure design

In order to satisfy the need for equal structural displacement in the design of support structures in fine optoelectronic tracking devices,this paper proposes a structural topology optimization model based on the SIMP method with maximizing stiffness as the objective while having the constraints of volume and equal displacement.The displacement equality constraints are introduced to the original objective function through the augmented Lagrangian multiplier method.When determining the Lagrangian multiplier,an approximate substitution method is used which considers its corresponding real physical meaning instead of the traditional pure mathematical iterative approximation method.By using the adjoint method,the augmented objective function sensitivity is obtained.And by applying the MMA optimization algorithm,the design variables are updated while satisfying the volume constraint.Finally,numerical examples are presented to illustrate the effectiveness of the method in designing lightweight structures with maximum stiffness and multiple displacement constraints.