结构拓扑优化局部性能约束下轻量化问题的互逆规划解法  

Reciprocal programming method for structural lightweight topology optimization with local performance constraints

作　　者：隋允康[1] 彭细荣[2] 叶红玲[1] 李宗翰 SUI Yun-kang;PENG Xi-rong;YE Hong-ling;LI Zong-han(Faculty of Materials and Manufacturing,Beijing University of Technology,Beijing 100022,China;School of Civil Engineering,Hunan City University,Yiyang 413000,China)

机构地区：[1]北京工业大学材料与制造学部,北京100022 [2]湖南城市学院土木工程学院,益阳413000

出　　处：《计算力学学报》2021年第4期479-486,共8页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(11672103,11872080);北京市自然科学基金(3192005)资助项目.

摘　　要：瞄准应力和疲劳两类局部性能约束的结构拓扑优化问题,概括为分部、化整和集成3种解法和交融的3种解法。类比应力约束推导了疲劳寿命情况,一为满疲劳公式,二为疲劳寿命约束全局化的结构寿命概念和相应解法。在倒寿命概念下,实现了疲劳寿命约束与应力约束的规格统一。补充和完整了已有的局部性能约束解法,属于单目标模型,有分部、化整、集成三种。基于互逆规划理论的定理2,提出了交融优化解法,是单目标与多目标模型的交替迭代,有分部-集成、化整-集成和集成-集成三种。上述6种解法皆基于ICM方法进行建模。算例表明,新提出的交融优化方法提高了求解效率。The structural topology optimization problem targeting the local performance constraints on stress and fatigue is summarized as three kinds of solutions:partition,globalization and integration methods,and three blending optimization methods.Fatigue life conditions are derived by analogy with stress constraints;one is full fatigue formula;the other is the concept of structural life with the globalization of fatigue life constraints and corresponding solutions.Under the concept of reverse life,the specification of fatigue life constraint and stress constraint is unified.The existing methods solving local performance constraint problems are supplemented.Three kinds of methods belong to the single objective model,which are partition,globalization and integration methods.Based on Theorem 2 of the reciprocal programming theory,three blending optimization methods are proposed,which are alternating iteration of single-objective and multi-objective models.They are partition-integration,globalization-integration and integration-integration blending optimization respectively.The above six methods are all modeled based on the ICM method.The numerical example shows that the proposed blending optimization methods can improve the solution efficiency.

关 键 词：局部性能约束 交融解法 互逆规划 分部解法 化整解法 集成解法 结构拓扑优化 ICM方法 

分 类 号：O343.1[理学—固体力学]