Discontinuous solutions in BEM for plate analysis in reissner-mindlin theory

Abstract

We present a new direction in the indirect Boundary Element Method (BEM), based on discontinuous solutions. These solutions were obtained by Prof. Moraru Gheorghe by applying the generalized Fourier transform to the differential equation of plates. Using these solutions as Green Influence functions we can solve plate bending problems that other analytical and numerical methods have no solution or have solving difficulties, for example: plates of arbitrary shapes and types of support, different loads, the presence of defects etc. For the proposed method, we performed a numerical implementation of the discontinuous solutions and developed a computational program in the Matlab programming language. In order to highlight the effect of transverse shear deformations on the deflection in Reissner-Mindlin plate theory, using this program, we calculated the displacements and stresses in square plates for different ratios of thickness to side length. The obtained results were compared with the Finite Element Method (FEM) and with analytical solutions (Fourier trigonometric series) in the classical plate theory.