关键词: 多边形单元, 插值函数, 积分方案, Gauss积分, Koyna重力坝

Abstract: 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.

Key words: polygonal elements, interpolation function, integration scheme, Gauss integral, Koyna gravity dam