Approaching analytical solution to elastic stress field of an#br#
infinite plane containing a single hole
ZHU Dayong1，2，CAI Yongxiang1，2
(1. College of Civil Engineering，Hefei University of Technology，Hefei，Anhui 230009，China；2. Anhui Key Laboratory of Civil Engineering and Materials，Hefei University of Technology，Hefei，Anhui 230009，China)
Abstract：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.
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2017, Vol. 36 
