裂缝分析的比例边界有限元与有限元耦合的虚拟结构面模型

比例边界有限元法SBFEM(Scaled Boundary Finite Element Method)是一种半解析数值方法,在裂缝分析特别是强度因子计算上具有相当高的精度。本文提出了一种用于裂缝分析的基于虚拟结构面的SBFEM与常规FEM的耦合分析方法。首先选取裂缝周边一定范围的计算域,并将结构分成不含裂缝区域和含裂缝区域两部分。然后,对不含裂缝区域,采用FEM进行网格离散;对含裂缝区域,采用SBFEM进行网格离散;两者相互独立,在这两个域内,分别采用各自相应的位移模式。最后通过在SBFEM网格的外边界设置虚拟耦合结构面的模式,实现有限元网格和比例边界有限元网格的耦合。通过两个经典的含裂缝平板的算例研究,探讨了本文方法在I型开裂和混合型开裂分析中,影响应力强度因子精度的因素。算例表明,SBFEM具有的降维和半解析性质,使本文方法在裂缝分析中的前处理简单易行,且计算结果具有相当高的计算精度。

Coupled SBFEM and FEM for crack analysis based on virtual discontinuous surface method

The newly-developed scaled boundary finite element method (SBFEM) is well in calculating stress intensity factors directly and precisely because the singularity in stress solutions crack tips is analytically represented.This study develops a novel virtual discontinuous surface method that couples the finite element method (FEM) and the scaled boundary finite-element method (SBFEM) for crack propagation modelling.Firstly,the structure containing cracks is divided into two independent zones,one contains cracks is discrete with SBFEM meshes and another without crack is discrete with FEM meshes.Then,the corresponding displacement interpolation models are used for each mesh respectively.At last,the virtual discontinuous surface will be utilized between the two zones for the coupling of SBFEM and FEM.The accuracy factors of this method,such as the shape,element size within SBFEM domain,are studied by simulations of two classic cracked plates.The example studies indicate that the pre-processing of this new method is quite simple,and calculated precision is relatively high.