Finite element analysis of infinite solids using elastic supports

Abstract

A highly efficient technique was recently developed for the finite element analysis of unbounded elastic solids by using multiple springs at the truncation surface. The treatment of negative stiffnesses of springs was based on an approximation and, therefore, a relatively larger extent of the infinite mass had to be discretized. In this paper it is shown that the negative stiffnesses may be accompanied by a singularity and that, in such cases, the main source of numerical errors is the singularity and not the negative stiffnesses. A very simple and highly effective procedure is proposed to treat the singularity without using any approximation. The proposed technique is tested by computing displacements and stresses around ‘deep’ circular underground openings in rock subject to different initial stress conditions. For all the cases analysed, results obtained by the proposed method are found to be almost identical to the closed-form solutions. The method may be applied to a wide variety of problems in geomechanics and in the analysis of stress concentration.