三维无网格Galerkin结构分析方法及其应用研究

Study on three-dimensional structure analysis method and application of element-free Galerkin method

针对无网格Galerkin法在三维复杂几何形状的结构分析中存在的刚度矩阵的稀疏存储实现难、六面体背景网格适应性差等问题,本文采用逐节点对法组装刚度矩阵,利用CSR格式存储刚度矩阵,提出了一种基于四面体背景积分的改进的三维无网格Galerkin法。通过采用罚函数法施加对称约束和给定位移值约束,并推导出了施加这两种位移约束的统一格式。利用所提算法完成了三维悬臂梁的计算,所得结果与其理论解相吻合;完成了轴流式风机轮毂的结构分析,得到的位移与应力分布结果与其有限元解相吻合。这表明本文所提方法能满足工程应用中的计算要求,并适用于具有复杂形状的几何模型分析。

Aiming at the problems that sparse storage capacity of stiffness matrix is bigger and the adaptability of hexahedral background grid is poor, the three dimensions element-free Galerkin method based on tetrahedron background integral grid is presented by using node pair-wise approach to assemble stiffness matrix and CSR format to store stiffness matrix. The penalty function method is used to impose the symmetry constraints and the displacement constraints with given values, and a computational scheme applied these two kinds of displacement constraints is derived. The calculation of three-dimensional cantilever beam is achieved by using the proposed algorithm in this paper, and the results obtained are in good agreement with the theoretical solutions. The structural analysis of axial fan hub is finished; the displacement and stress distribution of hub are in correspondence with their solutions of finite element. It shows that the proposed EFG method can meet the requirement of engineering calculation, and can be applied to the analysis of models with complex geometric shapes.