基于多边形最优一致逼近形式的上限有限元法  

The Upper Bound Finite Element Method Based on the Best Uniform Approximation Polygon Form

作　　者：孙聪 李菲菲 王延涛 SUN Cong;LI Feifei;WANG Yantao(Wuhan Ecological Environment Design and Research Institute Co.Ltd.,Wuhan 430050,Hubei,China)

机构地区：[1]武汉生态环境设计研究院有限公司,湖北武汉430050

出　　处：《江汉大学学报（自然科学版）》2023年第3期87-96,共10页Journal of Jianghan University：Natural Science Edition

基　　金：中国科学院国防科技创新基金项目(CXJJ-16M272)。

摘　　要：传统的上限有限元法采用外切多边形来逼近摩尔库伦屈服圆,该方法只有当多边形边数足够多时计算结果才比较精确,这往往导致线性规划规模过大,收敛速度较慢,给工程应用造成一定的影响。针对此问题,放松任意一点均须从上方严格收敛的上限性质,采用多边形最优一致逼近的形式构造线性化屈服函数和塑性流动方程。算例证明该方法求解规模更小,收敛速度大大提高。The traditional upper bound finite element method uses circumscribed polygons to approximate the Mohr-Coulomb yield circle.The calculation results are more accurate only when the number of polygon sides is sufficient,which often leads to the excessive scale of linear programming and slow convergence speed.It has a certain impact on engineering applications.So we relaxed the requirements that all the points must strictly meet the limit properties.The best uniform approximation polygon form was adopted to construct the linearized yield function and plastic flow equation.The numerical example showed that the method used could get a precise result by less number of polygon edges,and could greatly improve the convergence speed.

关 键 词：极限分析上限法 摩尔库伦屈服圆 线性规划 最优一致逼近 计算效率 

分 类 号：TU43[建筑科学—岩土工程]