全空间中粒子和裂纹的对偶边界积分方程及数值解

doi:10.3969/j.issn.1007-2861.2015.02.020

上海大学学报(自然科学版) ›› 2016, Vol. 22 ›› Issue (5): 533-544.doi: 10.3969/j.issn.1007-2861.2015.02.020

• 数理化科学 • 下一篇

全空间中粒子和裂纹的对偶边界积分方程及数值解

马杭1, 潘蒙2

1. 上海大学理学院, 上海200444;
2. 上海大学上海市应用数学和力学研究所, 上海200072

收稿日期:2015-05-11 出版日期:2016-10-31 发布日期:2016-10-31
通讯作者: 马杭(1951—), 男, 教授, 博士生导师, 博士, 研究方向为计算固体力学. E-mail: hangma@staff.shu.edu.cn
作者简介:马杭(1951—), 男, 教授, 博士生导师, 博士, 研究方向为计算固体力学. E-mail: hangma@staff.shu.edu.cn
基金资助:
国家自然科学基金资助项目(11272195, 11332005)

Dual boundary integral equations and numerical solutions for particles and cracks in full space

MA Hang1, PAN Meng2

1. College of Sciences, Shanghai University, Shanghai 200444, China;
2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Received:2015-05-11 Online:2016-10-31 Published:2016-10-31

摘要/Abstract

摘要：

针对弹性固体中同时含有粒子和裂纹的情况, 建立了全空间中的粒子和裂纹的位移间断形式的对偶边界积分方程计算模型, 解决了全空间条件下难以对研究对象进行直接加载的问题. 采用边界积分方程的离散形式对含有少量粒子和裂纹的典型情况进行了数值分析, 其中对粒子边界(或界面)和裂纹面分别采用边界点法和高斯配点法进行离散, 计算了裂纹的应力强度因子, 探讨了粒子与裂纹的相互作用. 通过与已有研究结果比较, 验证了计算模型与计算机程序的正确性与可靠性.

关键词: 对偶边界积分方程 , 数值解 , 应力强度因子, 粒子, 裂纹

Abstract:

As elastic solids contain particles and cracks, a computational model is proposed for the analysis of particles and cracks in full space using dual boundary integral equations in the displacement discontinuity formulation. The method avoids the difficulty of loading the objects under study in full space. Numerical analysis is carried out for some typical cases with a few particles and cracks using a discrete form of boundary integral equations. A boundary point method and Gauss collocation are used for discretization of the particle boundary or interface, and the crack surface, respectively. The stress intensity factors of cracks are computed. Mutual effects between particles and cracks are investigated and compared with those in the literature, verifying correctness and reliability of the proposed computational model and the program.

Key words: numerical solution , dual boundary integral equation , stress intensity factor, crack , particle

马杭1, 潘蒙2. 全空间中粒子和裂纹的对偶边界积分方程及数值解[J]. 上海大学学报(自然科学版), 2016, 22(5): 533-544.

MA Hang1, PAN Meng2. Dual boundary integral equations and numerical solutions for particles and cracks in full space[J]. Journal of Shanghai University（Natural Science Edition）, 2016, 22(5): 533-544.

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全空间中粒子和裂纹的对偶边界积分方程及数值解

Dual boundary integral equations and numerical solutions for particles and cracks in full space

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