CHEN Shenshen, WANG Juan. Application of a Coupled Interpolating Element-Free Galerkin Scaled Boundary Method and Finite Element Method in Fracture Analysis of Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2018, 39(11): 1258-1267. doi: 10.21656/1000-0887.390129
 Citation: CHEN Shenshen, WANG Juan. Application of a Coupled Interpolating Element-Free Galerkin Scaled Boundary Method and Finite Element Method in Fracture Analysis of Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2018, 39(11): 1258-1267.

# Application of a Coupled Interpolating Element-Free Galerkin Scaled Boundary Method and Finite Element Method in Fracture Analysis of Piezoelectric Materials

##### doi: 10.21656/1000-0887.390129
Funds:  The National Natural Science Foundation of China(11462006; 21466012)
• Rev Recd Date: 2018-05-21
• Publish Date: 2018-11-01
• 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.
•  [1] 平学成, 陈梦成, 谢基龙, 等. 基于新型裂尖杂交元的压电材料断裂力学研究[J]. 力学学报, 2006,38(3): 407-412.(PING Xuecheng, CHEN Mengcheng, XIE Jilong, et al. Fracture mechanics researches on piezoelectric materials based on a novel crack-tip hybrid finite element method[J]. Chinese Journal of Theoretical and Applied Mechanics,2006,38(3): 407-412.(in Chinese)) [2] LI C, MAN H, SONG C M, et al. Fracture analysis of piezoelectric materials using the scaled boundary finite element method[J]. Engineering Fracture Mechanics,2013,97(1): 52-71. [3] LI Q H, CHEN S S, LUO X M. Steady heat conduction analyses using an interpolating element-free Galerkin scaled boundary method[J]. Applied Mathematics and Computation,2017,300: 103-115. [4] 陈莘莘, 童谷生, 万云. 弹性力学问题的插值型无单元伽辽金比例边界法[J]. 中国科学： 物理学 力学 天文学, 2017,47(3): 034601.(CHEN Shenshen, TONG Gusheng, WAN Yun. An interpolating element-free Galerkin scaled boundary method for the elasticity problem[J]. Scientia Sinica: Physica, Mechanica & Astronomica,2017,47(3): 034601.(in Chinese)) [5] 陈莘莘, 王娟. 压电裂纹的插值型无单元伽辽金比例边界法分析[J]. 机械工程学报, 2017,53(6): 53-59.(CHEN Shenshen, WANG Juan. Analysis of interpolating element-free Galerkin scaled boundary method for piezoelectric cracks[J].Journal of Mechanical Engineering,2017,53(6): 53-59.(in Chinese)) [6] 王伟, 伊士超, 姚林泉. 分析复合材料层合板弯曲和振动的一种有效无网格方法[J]. 应用数学和力学, 2015,36(12): 1274-1284.(WANG Wei, YI Shichao, YAO Linquan. An effective meshfree method for bending and vibration analyses of laminated composite plates[J]. Applied Mathematics and Mechanics,2015,36(12): 1274-1284.(in Chinese)) [7] 王峰, 周宜红, 郑保敬, 等. 基于滑动Kriging插值的MLPG法求解结构非耦合热应力问题[J]. 应用数学和力学, 2016,37(11): 1217-1227.(WANG Feng, ZHOU Yihong, ZHENG Baojing, et al. A meshless local Petrov-Galerkin method based on the moving Kriging interpolation for structural uncoupled thermal stress analysis[J]. Applied Mathematics and Mechanics,2016,37(11): 1217-1227.(in Chinese)) [8] 肖毅华, 张浩锋, 平学成. 无网格对称粒子法中两类热边界条件的处理[J]. 华东交通大学学报, 2014,31(4): 65-70.(XIAO Yihua, ZHANG Haofeng, PING Xuecheng. Treatments of two kinds of thermal boundary conditions in meshless symmetric particle method[J]. Journal of East China Jiaotong University,2014,31(4): 65-70.(in Chinese)) [9] SONG C M. A matrix function solution for the scaled boundary finite element equation in statics[J]. Computer Methods in Applied Mechanics and Engineering,2004,193: 2325-2356. [10] DEEKS A J, WOLF J P. A virtual work derivation of the scaled boundary finite element method for elastostatics[J]. Computational Mechanics,2002,28(6): 489-504. [11] WANG J F, SUN F X, CHENG Y M. An improved interpolating element-free Galerkin method with a nonsingular weight function for two-dimensional potential problems[J]. Chinese Physics B,2012,21(9): 090204. [12] WANG J F, WANG J F, SUN F X, et al. An interpolating boundary element-free method with nonsingular weight function for two-dimensional potential problems[J]. International Journal of Computational Methods,2013,10(6): 1350043. [13] LANCASTER P, SALKAUSKAS K. Surface generated by moving least squares methods[J]. Mathematics of Computation,1981,37(155): 141-158. [14] 殷德胜, 尹栓, 周宜红. 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[J]. 计算力学学报, 2014,31(6): 735-741.(YIN Desheng, YIN Shuan, ZHOU Yihong. Coupled SBFEM and FEM for crack analysis based on virtual discontinuous surface method[J]. Chinese Journal of Computational Mechanics,2014,31 (6): 735-741.(in Chinese)) [15] YANG Z J, WANG X F, YIN D S, et al. A non-matching finite element-scaled boundary finite element coupled method for linear elastic crack propagation modelling[J].Computers & Structures,2015,153(C): 126-136. [16] 张雄, 刘岩. 无网格法[M]. 北京: 清华大学出版社, 2004.(ZHANG Xiong, LIU Yan. Meshless Methods [M]. Beijing: Tsinghua University Press, 2004.(in Chinese)) [17] WANG B L, MAI Y W. A piezoelectric material strip with a crack perpendicular to its boundary surfaces[J]. International Journal of Solids and Structures,2002,39(17): 4501-4524.

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