有限元计算中疏密网格过渡方法研究

工程计算中出于节省计算量的目的,往往需要在一个有限元模型中布置粗细不同的网格。为保证计算结果的准确性,必须保证网格突变情况下的位移协调问题。本文工作之一是在强天驰界面过渡单元的基础上,引入虚拟节点和子单元,在子单元中应用节理元思想,提出了基于最小势能原理的弹簧节理单元法。简化了积分运算,避免了精度要求极高的坐标转换,从而提高了方法的精度和实用性;二是提出了基于位移约束的主从自由度法,简便实用,只需简单的矩阵运算即可实现。两种方法均实现了不同尺寸网格间位移的协调性和刚度的匹配,从而使之满足有限元收敛准则,且生成的刚度阵具有对称性及带状性。算例证明两种方法精度良好,并可方便地应用于求解大规模工程问题。

Two methods for transition between coarse and fine finite elements

The transition between coarse and fine meshes in a finite element model is essential for application of Finite Element Method(FEM) to large-scale engineering problems.Two techniques are presented,viz.the Springed Joint Method and the Master DOF(Degree of Freedom) Method.The former is based on Qiang Tianchi's interface coupled method which was founded according to the least potential energy method.As in the Joint Element Method,with fictitious nodes and sub elements technique employed,the integral in Qiang Tianchi's version is simplified and transition between two sets of coordinate systems which requires high precision is avoided.The latter utilizes displacement constraint and needs only simple matrix operation in application.Both methods guarantee the matching of displacement of stiffness between meshes of different density and the stiffness matrix is band-shaped and symmetrical.Numerical tests show both methods are of good precision and feasibility and can be employed in analysis of large-scale engineering problems.