塑性极限分析的不可微模型及其光滑化算法

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．

Nonsmooth Model for Plastic Limit Analysis and Its Smoothing Algorithm

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.