摘要
基于现代凸分析数学方法,本文系统地建立了塑性极限分析变分原理的统一理论。利用Legendre-Fenchel变换,导出了一对严格互补的界限定理,其中的不可压缩条件和屈服条件均在超势及互补超势意义下得以自然放松。理论结果揭示了上、下限定理间存在着优美的对称性。根据下限定理中互补超势的性质,构造了一系列关于安全因子的变分原理,并提出了一个有效的罚一对偶迭代称法。
Based on the theory of convex analysis, a unified theory for the variational principles of limit analysis is established in this paper. By using Fenchel transformation, a true complementary bounding theorem is obtained, it shows that there exists an elegant symmetry between.the primal and dual problems in this field. Based on the property of the superpo-tential in this theorem, various variational principles are constructed, and an efficient penalty-duality algorithm for limit analysis is suggested.
出处
《力学学报》
EI
CSCD
北大核心
1989年第3期306-315,共10页
Chinese Journal of Theoretical and Applied Mechanics
关键词
塑性
极限分析
统一理论
变分原理
Plastic limit analysis, variational principle, Convex analysis
