基于自然单元法的极限下限分析  

Lower Bound Limit Analysis Based on Natural Element Method

作　　者：王崴 赵丽 李睿智 张怡 任红萍[3] WANG Wei;ZHAO Li;LI Ruizhi;ZHANG Yi;REN Hongping(Department of Electrical and Mechanical Engineering,Shanxi Institute of Energy,Jinzhong 030600,Shanxi,China;School of Material Science and Engineering,Taiyuan University of Science and Technology,Taiyuan 030024,Shanxi,China;School of Applied Science,Taiyuan University of Science and Technology,Taiyuan 030024,Shanxi,China)

机构地区：[1]山西能源学院机电工程系,山西晋中030600 [2]太原科技大学材料科学与工程学院,山西太原030024 [3]太原科技大学应用科学学院,山西太原030024

出　　处：《力学季刊》2025年第1期108-117,共10页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(52274389);山西省自然科学基金(201901D111248);山西省高等学校教育教学改革与实践项目(J20241544)。

摘　　要：自然单元法是一种基于自然邻近插值的无网格方法,其形函数构造简单,且易于施加本质边界条件.基于极限分析理论和降维思想,建立了用自然单元法进行二维理想弹塑性结构极限下限分析的整套求解算法.极限下限分析中的弹性应力场由自然单元法直接求出,利用自然单元法弹塑性迭代的结果得到自平衡应力基矢量并构造出所需的自平衡应力场.极限下限问题被转化为一系列数学规划子问题,并采用复合形法直接求解.数值算例结果表明,将自然单元法应用于极限下限分析是可行有效的.The Natural Element Method(NEM)is a meshless method based on natural neighbor interpolation.This method offers the advantages of simple shape function construction and ease of applying essential boundary conditions.Utilizing dimensional reduction techniques,a methodology for conducting lower bound limit analysis on two-dimensional elastoplastic structures has been developed through the application of NEM.In the lower-bound limit analysis,the elastic stress field is directly obtained using the NEM.The selfequilibrated stress basis vectors are derived from the elastoplastic iteration results of the NEM,and the required self-equilibrated stress field is constructed.The whole solution process of the problem is transformed into a series of sub-problems of nonlinear programming,which are solved through the complex method.Numerical examples demonstrate that the application of the Natural Element Method to lower-bound limit analysis is both feasible and effective.

关 键 词：自然单元法 自然邻近插值 极限分析 自平衡应力场 复合形法 

分 类 号：O344[理学—固体力学] O241[理学—力学]