Approaching analytical solution to elastic stress field of an infinite plane containing multiple holes
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：The method of approaching analytical solution to the elastic stress field of an infinite plane containing a single hole was extended to containing multiple randomly distributed holes of convex shapes under the arbitrary loadings on inner boundaries. Based on the principle of stress superposition，the stress field of an infinite plane containing m holes was divided into m stress fields，each with a single hole，referred as the isolated hole. A series of virtual tractions acted on the inner boundaries of holes. For one isolated hole，the virtual tractions generate the additional tractions on the inner boundaries of the other isolated holes. The additional tractions on one hole generated by all the other isolated holes plus the virtual tractions should be equal to the actual tractions acting on this hole. An iteration procedure was proposed to compute the values of virtual traction associated with all the isolated holes until the solution was converged. The elastic stress field within the infinite plane containing multiple holes is thus obtained. The results of examples show that the stress field of engineering scale obtained with this method agrees well with those from the finite element method. The values of stresses extremely near the holes can be computed as well and the generalized stress intensity factor and the order of stress singularity are obtained by data fitting.
2016, Vol. 35 
