Nonlinear analysis for the polygonal element

As an important method for solving boundary value problems of differential equations, the finite element method (FEM) has been widely used in the fields of engineering and academic research. For two dimensional problems, the traditional finite element method mainly adopts triangular and quadrilateral elements, but the triangular element is constant strain element, its accuracy is low, the poor adaptability of quadrilateral element with complex geometry. The polygon element is more flexible and convenient in the discrete complex geometric model. Some interpolation functions of the polygon element were introduced. And some analysis was given. The numerical calculation accuracy and related features of different interpolation function were studied. The damage analysis for the koyna dam was given by using the polygonal element polygonal element of Wachspress interpolation function. The damage result is very similar to that by using Xfem, which shows the calculation accuracy of this method is very high.