基于可靠性指标法的连续体结构可靠性拓扑优化  

Reliability topology optimization of continuum structure based on reliability index method

作　　者：王林军 李家豪 张正伟[2] 吴振雨 魏悠贵 刘辉[4] WANG Lin-jun;LI Jia-hao;ZHANG Zheng-wei;WU Zhen-yu;WEI You-gui;LIU Hui(School of Mechanical and Power Engineering,China Three Gorges University,Yichang 443002,China;China Ship Scientific Research Center,Wuxi 214082,China;School of Mechatronic Engineering,Xi′an Technological University,Xi’an 710021,China;School of Civil and Architectural Engineering,Wuhan University,Wuhan 430072,China)

机构地区：[1]三峡大学机械与动力学院,宜昌443002 [2]中国船舶科学研究中心,无锡214082 [3]西安工业大学机电工程学院,西安710021 [4]武汉大学土木建筑工程学院,武汉430072

出　　处：《计算力学学报》2025年第1期98-105,共8页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(11202116,12072242,12372200)资助项目。

摘　　要：实际工程中,结构面临着来自多种复杂环境下不确定性因素的影响,导致结构性能的变化,传统拓扑优化未考虑这些因素的影响。因此,本文提出了一种可靠性指标法(RIA)的可靠性拓扑优化方法,用于连续体结构拓扑优化。旨在考虑结构可靠性的情况下,使得结构最终拓扑构型的体积分数最小。本文将载荷作为不确定量,通过可靠性指标法寻找极限状态点;然后基于双向渐进结构优化法(BESO),以结构体积为目标函数,可靠性指标作为约束条件,采用移动渐近线法(MMA)进行优化。对不同的数值算例(如简支梁、悬臂梁、L型梁)进行分析,同时研究了目标可靠度和标准差对结构性能的影响,还考虑了多工况、载荷方向不确定性等情况。研究结果表明,本文方法能够高效地找到极限状态点,相较于传统拓扑优化方法所得的拓扑构型更加可靠。In practical engineering,a structure is faced with the influence of uncertain factors from a variety of complex environments,which leads to the change of structural performance.Traditional topology optimization does not consider the influence of these factors.Therefore,this paper proposes a reliability topology optimization method for continuous structures based on a reliability index method(RIA).The aim is to minimize the volume fraction of the final topological configuration of the structure considering structural reliability.In this paper,the load is considered to be uncertain,and the limit state point is found by the reliability index method.Then,based on the bi-directional evolutionary structural optimization(BESO)method,the method of moving asymptotes(MMA)is used to optimize the structural volume as the objective function and the reliability index as the constraint condition.Through the analysis of different numerical cases(such as a simply supported beam,a cantilever beam,an L-shaped beam),the influence of the target reliability and the standard deviation on the structural performance is studied,and the uncertainty of multiple working conditions and load direction is also considered.The results show that the proposed method can efficiently find the limit state points,which is more reliable than the topological configuration obtained by the traditional topology optimization method.

关 键 词：可靠性指标法 移动渐进性法 变密度法 可靠性拓扑优化 

分 类 号：O302[理学—力学] O224