塑性极限分析的不可微模型及其光滑化算法  

Nonsmooth Model for Plastic Limit Analysis and Its Smoothing Algorithm

作　　者：李建宇[1] 潘少华[2] 李兴斯[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116023 [2]华南理工大学应用数学系,广州510641

出　　处：《应用数学和力学》2006年第8期940-946,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(1057203110332010)

摘　　要：藉助于凸规划的Lagrange对偶理论,建立了Mises屈服条件下理想刚塑性材料Hill最大塑性功原理的对偶问题,并据此建立了极限分析的一个不可微凸规划模型.该模型不仅避免了对屈服条件的线性化,而且其离散化形式为线性约束下Euclid模之和的极小化问题.针对Euclid模的不可微性,提出理想刚塑性体极限分析的一种光滑化算法.通过计算平面应力和平面应变问题的极限荷载因子和相应的坍塌机构,验证了算法的有效性.By means of Lagrange duality theory of the convex program, a dual problem of Hill＇s maximum plastic work principle under Mises＇ yielding condition was derived and whereby a non-differentiable convex optimization model for the limit analysis were developed. With this model, it is not necessary to linearize the yielding condition and its discrete form becomes a minimization problem of the sum of Euclidean norms subjected to linear constraints. Aimed at resolving the non-differentiability of Euclidean norms, a smoothing algorithm for the limit analysis of perfect-plastic continuum media was prposed. Its efficiency was demonstrated by computing the limit load factor and the collapse state for some plane stress and plain strain problems.

关 键 词：塑性极限分析 对偶 不可微优化 光滑化 

分 类 号：O344.5[理学—固体力学] O221.2[理学—力学]