Stress Analysis of Elastic Roof with Boundary Element Formulations

Roof is one of the most important structures in coal mining engineering, which needs to be studied thoroughly at the theoretical level, while elastic roof is treated as one of the problems for elastic plates in this paper. The existing literatures on elastic plates have largely restricted to different engineering but all most minority for coal mining engineering. Based on the mechanical models of plane and bending stress for elastic roof, using the boundary integral equations which is obtained by the natural boundary reduction, this paper obtains the elastic roof's Airy stress functions of the problem of inner elastic plane roof and bending deflection respectively, as well as the analytical and numerical solutions to the each stress field functions. We also analyze the rules of different stress distribution for the two stress fields varying with the radius and the angle by comparison. The results of calculation show that, with the increasing of the radius and the angles of the elastic circular plate roof with a pair of tensile forces along its diameter on the boundary, the value of the stress meets uniformity; with the increasing of radius, the stress declines under a concentrated force.