含单孔洞无限平面体弹性应力场解析逼近方法  

Approaching analytical solution to elastic stress field of an infinite plane containing a single hole

作　　者：朱大勇[1,2] 蔡永祥[1,2] ZHU Dayong CAI Yongxiang(College of Civil Engineering, Hefei University of Technology, Hefei , Anhui 230009, China Anhui Key Laboratory of Civil Engineering andMaterials, Hefei University of Technology, Hefei, Anhui 230009, China)

机构地区：[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

出　　处：《岩石力学与工程学报》2017年第3期705-715,共11页Chinese Journal of Rock Mechanics and Engineering

摘　　要：基于半无限平面体顶边集中力作用下的弹力应力解析解,提出一种解析逼近方法,求解含单个任意形状凸孔洞无限平面体在孔边任意荷载作用下的弹性应力场。将n边形孔洞外域划分为顶边上作用待定面力分布的n个半无限平面体。对于每个半无限平面体的顶边,其孔口部分外力已知,而两侧延伸部分上面力未知。提出一种有效的迭代方式依次计算所有延伸边上的面力,直至收敛,同时得到孔洞外域的弹性应力场。该方法原理简单、计算过程明了;由于基于弹性力学解析解和一维高精度数值积分,其最终结果属解析逼近解。算例表明,该方法获得的工程尺度下的孔洞外域应力场与复变函数方法、有限元方法计算结果非常吻合,表明方法的有效性。同时,可计算孔洞角点处近场应力,由孔洞角点处近场应力值拟合得到的广义应力强度因子具有极高精度,且应力奇异性次数与断裂力学理论值一致。On the basis of analytical solution of elastic stresses within a semi-infinite plane subjeted to the concentred loading on the surface, a approaching analytical solution is proposed for solving the elastic stress field of an infinite plane containing a single hole with arbitrary convex shape, subjected to arbitrary loading on the inner surfaces. The outer domain of a convex hole of n-polygon shape was divided into n semi-infinite planes. For the surface of every semi-infinite plane, the loadings on the inner surface of the hole is given with the traction to be determined on the extended surfaces into two adjacent semi-infinite planes. An effective iteration procedure is proposed for computing the values of traction on all the extended surfaces successively until the solution is converged, and the elastic stress field of the outer domain of the hole is thus determined. The presented method is simple in principle and computation process. As the computation is based on the analytical elastic solution and the one-dimensional numerical integration of high precision, the final result is approaching the analytical solution. The results of examples show that the stress field of engineering scale thus obtained with the proposed method agrees well with those from the finite element method and complex variable function method, illustrating the effectiveness of the method. The values of stresses in the near field around the hole can be computed as well, with which the generalized stress intensity factor and the order of stress singularity are fitted. The value of generalized stress intensity factor fitted is of high precision and the order of stress singularity is practically equal to the analytical solution in fracture mechanics.

关 键 词：岩石力学 单孔洞 无限平面体 半无限平面体 弹性应力 应力奇异性次数 广义应力强度因子 

分 类 号：TU45[建筑科学—岩土工程]