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K-S函数集成局部性能约束的结构拓扑优化二阶逼近解法
引用本文:彭细荣,隋允康,叶红玲,铁军.K-S函数集成局部性能约束的结构拓扑优化二阶逼近解法[J].固体力学学报,2022,43(3):307-317.
作者姓名:彭细荣  隋允康  叶红玲  铁军
作者单位:1. 湖南城市学院;2. 北京工业大学;
基金项目:国家自然科学基金项目(11672103,11172013);;湖南省自然科学基金项目(2022JJ30113)资助;
摘    要:应用K-S (Kreisselmeier–Steinhauser)函数,对结构拓扑优化问题中的局部性能如应力、疲劳寿命等进行集成然后求解。首先针对互逆规划的单目标多约束模型(称为s方模型)及多目标单约束模型(称为m方模型),应用结构拓扑优化ICM方法,分别建立了基于K-S函数集成处理的优化模型,推导了集成化的约束(对s方模型)或目标(对m方模型)函数的一阶及二阶导数,采用序列二次规划模型对所建立的优化模型进行迭代求解,依据K-T条件给出了二次规划模型的迭代求解公式。然后基于K-S函数阐述了s方模型的集成迭代解法,亦即集成方法。最后,阐述了基于K-S函数的s方模型和m方模型交替融合的迭代解法,亦即集成-集成方法。结果表明集成-集成方法比单纯的集成方法收敛更快。

关 键 词:局部性能  结构拓扑优化  K-S函数  优化模型的二阶逼近  ICM方法  local  performance    structural  topology  optimization    K-S  function    second-order  approximation  of  optimization  models    ICM  method  
收稿时间:2021-09-23

Second-order approximated alogrithm of using K-S function to intergrate local performance constraints in structural topology optimization
Abstract:The K-S ( Kreisselmeier-Steinhauser ) function is used to integrate local performances such as stress and fatigue life in structural topology optimization; and then a method of solving the model was proposed. First, for the single objective and multiple constraints model ( called s-model ) and multiple objective and single constraint model ( called m-model ) in the inverse programming, optimization models are established by utilizing K-S function integration based on the ICM method. The first and second order derivatives of constraint ( s-model ) and objective ( m-model ) functions on design variables are deduced. The sequential quadratic programming model is used to solve the optimization model iteratively. The iterative formula for quadratic programming model is given according to the K-T condition. Then, based on the K-S function integration, the iterative solution to s-model is described, that is, the integration method. Finally, based on K-S function integration, the iterative solution to s-model and m-model alternately is described, that is, the integration-integration method. The results show that the integration-integration method converges faster than the integration method.
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