O método dos elementos de contorno aplicado às teorias de placas de Reissner, Mindlin e Reddy

Abstract

In this work, the Boundary Element Method (BEM) is applied to Reissner, Mindlin, and Reddy’s plate theories. At first, the Reissner and Mindlin theories are discussed, where a purê formulation of the BEM is proposed extending the application of the Multiple Reciprocity Method (MRM) to shear deformable plates governed by Reissner and Mindlin hypotheses when subjected to arbitrary polynomial distributed loads. In addition, fundamental high-order solutions that are essential in the MRM technique are deduced recursively and explicitly for all required orders. In a second step, a regular formulation of the BEM for third-order shear plates is proposed, where Reddy’s hypotheses are taken into account. In addition, the integral equations and fundamental solutions, in displacements and forces, are deduced as well as the description of the formation of the algebraic system of the BEM for the problem using linear and circular elements. Numerical examples of plates are presented in order to validate the computational implementation performed in the two plate theories. The results presented for different loading cases and boundary conditions validate the BEM formulation presented for the Reissner, Mindlin, and Reddy’s plate theories