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。
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.
作者
乔楠
谢军
王强龙
刘震宇
QIAO Nan;XIE Jun;WANG Qiang-long;LIU Zhen-yu(Changchun Institute of Optics,Fine Mechanics and Physics,Chinese Academy of Science,Changchun 130033,China;College of Materials Science and Opto-Electronic Technology,University of the Chinese Academy of Sciences,Beijing 100039,China)
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2019年第6期721-726,共6页
Chinese Journal of Computational Mechanics
基金
国家自然科学基金(51675506)资助项目
关键词
位移等式约束
增广拉格朗日乘子
反作用力
拓扑优化
光电精密设备
displacement equality constraints
augmented Lagrangian multiplier
reaction force
topology optimization
fine optoelectronic devices
