Abstract
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.
Highlights
The finite element method (FEM) is commonly utilized in engineering and academic research fields
The polygonal element is more flexible and convenient in the discrete complex geometric model and it can simulate the mechanical properties of a given material
We compared the results yielded by the various kinds of polygonal element analysis and suggested the kinds of the shape function and numerical integrations as well as the number of integral points of polygonal element
Summary
The finite element method (FEM) is commonly utilized in engineering and academic research fields. The polygonal element is more flexible and convenient in the discrete complex geometric model and it can simulate the mechanical properties of a given material (see [1,2]). The polygonal element has the geometric flexibility which makes it suitable for simulating crack growth. It can be utilized to solve problems related to fracture and large-deformation, frictionless, dynamic, contact-impact of arbitrary geometries and boundaries (see [3,4]). The polygonal element and Voronoi FEM have favorable accuracy in solving plastic problems with small deformation (see [5]). We exploited the afore-mentioned advantages of the polygonal element for the numerical analysis of a practical engineering problem. We compared the results yielded by the various kinds of polygonal element analysis and suggested the kinds of the shape function and numerical integrations as well as the number of integral points of polygonal element
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