Application of a Coupled Interpolating Element-Free Galerkin Scaled Boundary Method and Finite Element Method in Fracture Analysis of Piezoelectric Materials
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摘要: 插值型无单元Galerkin比例边界法是一种只需在边界上采用插值型无单元Galerkin法离散且无需基本解的半解析方法,能有效求解压电材料的断裂问题.为进一歩提高这种方法的适用性,该文提出了一种用于压电材料断裂分析的插值型无单元Galerkin比例边界法耦合有限元法(finite element method, FEM)的分析方法.裂纹周边一定范围的计算域采用插值型无单元Galerkin比例边界法离散,其余区域采用FEM离散.插值型无单元Galerkin比例边界法方程和FEM方程的耦合可利用界面两侧广义位移的连续条件方便地实现.最后,给出了两个数值算例验证了该文所提方法的有效性.
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关键词:
- 压电材料 /
- 断裂力学 /
- 插值型无单元Galerkin比例边界法 /
- 强度因子
Abstract: The interpolating element-free Galerkin scaled boundary method (IEFG-SBM) is a semi-analytical method which only requires discretizing the boundary with the interpolating element-free Galerkin (EFG) method without fundamental solution. This method is very powerful to deal with fracture problems of piezoelectric materials. In order to further improve the applicability of the IEFG-SBM, a coupled IEFG-SBM and finite element method (FEM) for fracture analysis of piezoelectric materials was developed. The IEFG-SBM was utilized to model the domain close to the crack tip and the FEM was employed in the remaining domain. Based on continuity conditions at the interface between the IEFG-SBM sub-domain and the FEM sub-domain, the coupled formula of the proposed method can be conveniently derived. Finally, 2 numerical examples were presented to demonstrate the validity of the proposed method. -
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