摘要
有限元方法是材料力学性能分析的主要工具。对于颗粒增强复合材料,其增强相或夹杂多为不规则的多边形,共采用经典有限元分析,需划分稠密的计算网格,降低分析效率。本文以多边形为有限元计算单元,采用Wachspress作为试函数,建立分析非均质材料力学性能的多边形有限元方法,给出形函数计算的简化公式。多边形单元的位移插值采用Wach-spress插值,能自动满足不同形状单元间的协调性。计算网格按照材料分布的真实结构划分为若干多边形单元。数值算例验证了多边形有限元在模拟非均质材料力学性能方面的有效性和计算精度。
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.
出处
《玻璃钢／复合材料》
CAS
CSCD
北大核心
2007年第5期11-15,共5页
Fiber Reinforced Plastics/Composites
基金
山东建筑工程学院博士基金
科研基金项目(XN050103)
