Analysis of interpolating element-free Galerkin scaled boundary method for fracture problems in orthotropic materials

doi:10.19936/j.cnki.2096-8000.20230228.004

Abstract

Abstract: The interpolating element-free Galerkin scaled boundary method is a semi-analytical numerical method which combines the advantages of the scaled boundary method and the element-free Galerkin method under the framework of improved interpolating moving least-squares method. By introducing the scaled boundary coordinate system, this method only needs to perform numerical discretization on the boundary of the computational domain and solve the problem by using the analytical method in the radial direction, which has considerable accuracy and efficiency in analyzing the fracture problem of isotropic materials. In order to make full use of the virtues of this method and improve its service ability, the interpolating element-free Galerkin scaled boundary method is proposed to study the fracture of orthotropic materials. Finally, two numerical examples of different crack forms are used to certify the effectiveness and precision of the method.

Key words: interpolating element-free Galerkin scaled boundary method, orthotropic materials, fracture problems, stress intensity factor, composites

CLC Number:

TB332

WANG Juan, CHEN Yang, XIAO Shucong. Analysis of interpolating element-free Galerkin scaled boundary method for fracture problems in orthotropic materials[J]. COMPOSITES SCIENCE AND ENGINEERING, 2023, 0(2): 34-38.

References

[1] TAN C L, GAO Y L. Boundary element analysis of plane anisotropic bodies with stress concentrations and cracks[J]. Composite Structures, 1992, 20(1): 17-28.
[2] BAYAT S H, NAZARI M B. Thermal fracture analysis in orthotropic materials by XFEM[J]. Theoretical and Applied Fracture Mechanics, 2021, 112: 102843.
[3] 王永亮, 王建辉, 张磊. 含多裂纹损伤圆弧曲梁自由振动扰动的有限元网格自适应分析[J]. 工程力学, 2021, 38(10): 24-33.
[4] 滕靓媚, 黄君, 黄立新. 基于分层法石墨烯增强功能梯度梁的有限元分析[J]. 复合材料科学与工程, 2022(1): 13-21.
[5] 陈莘莘, 钟斌. 二维黏弹性力学问题的无网格自然单元法[J]. 应用数学和力学, 2017, 38(5): 605-612.
[6] 王冰冰, 高欣, 段庆林. 稳态热传导的二阶一致无网格法[J]. 应用数学和力学, 2013, 34(7): 750-755.
[7] 陈莘莘, 王娟. 插值型无单元Galerkin比例边界法与有限元法的耦合在压电材料断裂分析中的应用[J]. 应用数学和力学, 2018, 39(11): 1258-1267.
[8] 陈莘莘, 周文博, 胡常福. 基于插值型无单元Galerkin法的复合材料层合板自由振动分析[J]. 应用力学学报, 2021, 38(3): 1280-1285.
[9] 王涛, 陈莘莘. 粘弹性问题的插值型无单元伽辽金比例边界法[J]. 力学季刊, 2021, 42(3): 507-516.
[10] WOLF J P, SONG C M. The scaled boundary finite-element method-a fundamental solution-less boundary-element method[J]. Computer Methods in Applied Mechanics & Engineering, 2001, 190(42): 5551-5568.
[11] 章鹏, 杜成斌, 江守燕. 比例边界有限元法求解裂纹面接触问题[J]. 力学学报, 2017, 49(6): 1335-1347.
[12] 曾亿山, 卢德唐, 曾清红. 无单元伽辽金法的并行计算[J]. 计算力学学报, 2008, 25(3): 385-391.
[13] ZHANG Z, LIEW K M, CHENG Y M, et all.Analyzing 2D fracture problems with the improved element-free Galerkin method[J]. Engineering Analysis with Boundary Elements, 2008, 32(3): 241-250.
[14] SUN F X, WANG J F, CHENG Y M. An improved interpolating element-free Galerkin method for elasticity[J]. Chinese Physics B, 2013, 22(12): 47-54.
[15] 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.
[16] 陈莘莘, 王娟. 反平面断裂问题的无单元伽辽金比例边界法[J]. 计算力学学报, 2017, 34(1): 57-61.
[17] 陈莘莘, 王娟. 断裂问题的插值型无单元伽辽金比例边界法与有限元法的耦合研究[J]. 中国科学: 物理学力学天文学, 2018, 48(2): 48-56.
[18] 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): 83-90.
[19] 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(23-26): 2325-2356.
[20] SONG C M, WOLF J P. Semi-analytical representation of stress singularities as occurring in cracks in anisotropic multi-materials with the scaled boundary finite-element method[J]. Computers and Structures, 2002, 80(2): 183-197.
[21] ASADPOURE ALIREZA, MOHAMMADI SOHEIL, VAFAI ABOL-HASAN. Crack analysis in orthotropic media using the extended finite element method[J]. Thin-Walled Structures, 2006, 44(9): 1031-1038.