A pure boundary element analysis of Reissner's shear deformable plates subjected to higher-order polynomial loading

Abstract

In this paper, a direct Boundary Element Method (BEM) solution without load domain integrals for Reissner's plates subjected to higher-order polynomial loads is derived. To this end, the Multiple Reciprocity Method (MRM), which consists to transform original domain integrals into a series of equivalent boundary integrals using Green's second identity in a recursive way, is used. Moreover, higher-order fundamental solutions of thick plates in bending, which are essential in MRM technique, are also derived and presented in an explicit form for all terms of the series. Despite this present approach deals directly with higher-order polynomial distribution load, this boundary element solution can be also applied to other load distribution functions, since it is possible to expand them in a polynomial series. Numerical results are presented for differing cases of boundary conditions and load functions, such as linear, double quadratic, exponential, and double sinusoidal distributions. The BEM results are compared to analytical solutions showing good agreement among them.