基于SBFEM计算应力强度因子的叠单元法

Superposed element method for calculating stress intensity factors based on scaled boundary finite element method

基于SBFEM(scaled boundary finite element method,比例边界有限元法),提出了一种裂缝应力强度因子计算的叠单元法.对于含裂缝的结构,该方法首先将其离散为不含裂缝的整体FEM网格和包含裂缝及周边一定范围计算域的局部SBFEM网格,两者相互独立.然后,将整体网格和局部网格叠加,通过几何拓扑运算,可得单元间的相互关系.在局部SBFEM计算域内,采用SBFEM的位移模式;在SBFEM计算域之外,借鉴流形元的思路,采用有限元的位移插值模式.最后,通过在局部SBFEM网格外的边界施加虚拟结构面的模式,实现整体域网格和局部域网格的耦合.通过3个经典的含裂缝平板的算例研究,表明该方法能有效降低裂缝分析时的前处理的难度,且计算精度也较高.

This study develops a novel superposed element method that coupling the finite element method （FEM） and the scaled boundary finite element method （SBFEM） for calculating stress intensity factor. By using this method, the structure containing cracks is divided into two independent parts; one is the global FE mesh without cracks; and the other is the local SBFE mesh including the, cracks, and their adjacent zone. These two parts are then superposed together, and the relationship of elements between these two parts can be obtained by few simple calculation of geometric topology. The displacement interpolation of SBFEM is used in the local zone and the FEM is used in the global zone; the two parts are coupled at the outer boundaries of the local SBFE mesh, with the virtual discontinuous surface method. Three classic cracked plates are studied; it is shown that the pre-processing of this new method is quite simple; and calculation precision is relatively high.