关键词: 非均质材料, 数值模拟, 多边形单元, Wachspress插值, 多边形有限元法

Abstract:

The popular tool to analyze mechanical properties of materials is finite element method.For particulate-reinforced composite material,the reinforced phases or inclusions are usually irregular polygons.Owing to partition dense finite elements by classically FEM to simulate heterogeneous materials,it decreases the computational efficiency.In this paper,by using polygons as computational elements and applying rational functions as trial and test functions,the polygonal finite element method for heterogeneous materials simulation is presented.The reduce formulations of Wachspress interpolation shape functions are given.Applying Wachspress interpolations as displacement functions of polygonal elements,the interelement compatibility of displacements can be automatically ensured.According to the real structure of materials,the computational grids contain some polygonal elements.Numerical examples are presented to demonstrate the performance and accuracy of the polygonal finite element method.

Key words: heterogeneous materials, numerical simulation, polygonal elements, wachspress interpolation, polygonal finite element method