有限元中多边形单元的研究及应用  

Research and application of polygonal elements in FEM

作　　者：徐强[1,2] 张桂彬 陈健云[1,2] 李静[1,2] ZHANG Peilun;LEI Xiaohui;WANG Xu;WANG Chao(State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin,China Institute of Water Resources and Hydropower Research,Beijing 100038,China)

机构地区：[1]大连理工大学海岸与近海工程国家重点实验室,辽宁大连116024 [2]大连理工大学工程抗震研究所,辽宁大连116024

出　　处：《人民长江》2018年第12期77-86,共10页Yangtze River

基　　金：国家重点研发计划项目"300 m级特高坝抗震安全评价与控制关键技术"(2017YIC0404903);大连市高层次人才创新支持计划项目"大坝的多尺度算法的研究"(2016RQ015);国家自然科学基金项目"胶凝砂砾石坝强震失效模式及振动台模型试验基础研究"(51679030)

摘　　要：详细介绍了3种常用的多边形插值函数,并给出了两种数值精度较高的多边形有限元的积分方案。通过小片实验,研究了多边形单元的数值精度与积分点个数的关系、不同插值函数的数值精度以及对网格尺寸的敏感性。通过求解厚壁圆筒问题,对比分析了多边形单元和四边形单元的数值精度。随后将多边形单元应用到Koyna重力坝的数值分析中。结果表明:所提出的多边形单元在单元数较少的情况下就可达到较高的计算精度,相比于经典有限元,在相同精度下能减少计算量,节约内存。In this paper,three commonly used polygonal interpolation functions are introduced in detail,and two kinds of highly accuracy numerical integration schemes for polygonal finite elements are given. The relationship between the numerical accuracy and the number of integral points of polygonal elements,the numerical accuracy of the different interpolation functions and the sensitivity to the mesh size are studied by patch-test. By solving the issue of thick-walled cylinder,the numerical accuracies of polygonal element and quadrilateral element are compared and analyzed. Then the polygonal element is applied to the numerical analysis of Koyna gravity dam. The results show that the proposed polygonal elements have high accuracy even using relatively less elements; the polygonal elements can reduce the computational amount and save the memory for the same accuracy compared with the classical finite element.

关 键 词：多边形单元 插值函数 积分方案 GAUSS积分 Koyna重力坝 

分 类 号：TV642[水利工程—水利水电工程]