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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
Topology optimization with multiple displacement equality constraints and application in optoelectronic fine structure design
投稿时间:2018-11-16  修订日期:2018-12-21
DOI:
中文关键词:  位移等式约束  增广拉格朗日乘子法  反作用力  拓扑优化  光电精密设备
英文关键词:Displacement equality constraints  Augmented Lagrangian multiplier  Reaction force  Topology optimization  Fine optoelectronic devices
基金项目:国家自然科学基金项目(51675506)
作者单位E-mail
乔楠 中国科学院长春光学精密机械与物理研究所 1070719486@qq.com 
谢军 中国科学院长春光学精密机械与物理研究所  
王强龙 中国科学院长春光学精密机械与物理研究所  
刘震宇 中国科学院长春光学精密机械与物理研究所 liuzy@ciomp.ac.cn 
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中文摘要:
      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要求的设计,构建出基于变密度法的以刚度极大为目标、同时以体积约束和位移等式约束作为约束条件的结构拓扑优化模型。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迭代优化得到新结构。算例验证结果显示,该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。
英文摘要:
      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 maximum stiffness as objective while having the constraints of volume and equal displacement. The displacement equality constraints were introduced to the original objective function through the augmented Lagrangian multiplier method. When solving the Lagrangian multiplier, an approximate substitution method was 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 was obtained. And by applying the MMA optimization algorithm, the design variables are updated while satisfying the volumetric constraint. Finally, numerical examples were presented to illustrate the effectiveness of the method in designing lightweight structure with maximum stiffness and multiple displacement constraints.
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