A method of approaching analytical solution to elastic stresses of regular
polygon hole under symmetrical loading

ZHU Da-yong; CAI Yong-xiang

doi:10.16285/j.rsm.2016.S2.007

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A method of approaching analytical solution to elastic stresses of regular polygon hole under symmetrical loading

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- A method of approaching analytical solution to elastic stresses of regular polygon hole under symmetrical loading
- Vol. 37, Issue S2, Pages: 60-66(2016)
- 作者机构：
  
  1. 合肥工业大学土木与水利工程学院,安徽,合肥,230009
  2. 合肥工业大学土木工程结构与材料安徽省重点实验室,安徽,合肥,230009
- 作者简介：
- 基金信息：
- DOI：10.16285/j.rsm.2016.S2.007
  CLC： TB115
- Online First：09 June 2018，
  
  Published：2016
- 稿件说明：
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ZHU Da-yong, CAI Yong-xiang. A method of approaching analytical solution to elastic stresses of regular polygon hole under symmetrical loading[J]. 2016, 37(S2): 60-66.
DOI：

ZHU Da-yong, CAI Yong-xiang. A method of approaching analytical solution to elastic stresses of regular polygon hole under symmetrical loading[J]. 2016, 37(S2): 60-66. DOI： 10.16285/j.rsm.2016.S2.007.

摘要

提出一种简单有效的计算方法，求解对称荷载作用下含正多边形孔洞无限平面体的弹性应力解。将孔洞内边界向两侧延伸至应力可忽略的远处，其外侧构成半无限平面体。相邻两个半无限平面体有一个公共域，其中一个半无限平面体顶边延伸至相邻两个半限平面体体内。孔洞内边界上面力是已知的，延伸至两相邻半无限平面体体内的顶边上面力可先假设，由弹性理论求出半无限平面体体内应力，再计算相邻半无限平面体顶边上面力，根据对称性得到本半无限平面体顶边上面力改进值，迭代求解直至收敛。该方法具有计算过程简单、精度高等优点。算例分析表明，该方法求解的工程尺度下孔洞周边应力场与复变函数方法、有限元方法计算结果吻合，拟合计算的孔边角点处应力奇异性次数与理论解基本一致。

Abstract

A simple and effective method is proposed for elastic stress analysis of an infinite plane including a regular polygon hole

subjected to symmetrical loading on the hole boundaries. The inner boundary of the hole is extended to far point where the magnitude of stresses is negligible. The outer area of the boundary consists of a semi-infinite plane body. The adjacent two semi-infinite plane bodies share a common domain

the extending boundary of one semi-infinite plane body stretching into another. With the values of loadings on the inner boundaries of the hole known and the traction on the boundaries stretching into other semi-infinite plane bodies firstly presumed

the stress distribution within the semi-infinite plane body can be calculated using the theory of elasticity. By symmetry

the traction on the two boundaries stretching into adjacent semi-infinite plane bodies can be calculated

and further modified with iteration method

and converge to analytical solutions. The presented method features straightforward computation process and high precision. The results of presented examples show that the stresses of engineering scale thus obtained by this method agree well with ones obtamed by function of complex variable method and finite element method; and the order of stress singularity near the corner of hole is also approximately equal to theoretical value.

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