Shear deformable plate by SGBEM: Indirect “progenitor matrix” approach

Abstract

The Mindlin-Reissner’s formulation of shear deformable plate is addressed through the Symmetric Galerkin Boundary Element Method (SGBEM). The thick plate’s elastic problem is resolved and fundamental solutions matrix is obtained. The application of Betti’s theorem in the unlimited domain allows obtaining the Somigliana’s Identities (S.I.s). The solving system is obtained by an indirect approach, i.e., through the “progenitor matrix”. The “progenitor matrix” allows simulating all possible plate’s load conditions and is the starting point for an automatic calculation code. The coefficients are calculated through the theory of distributions, using double integrals without resorting to regularization techniques but by exploiting the expansion in power series of the Bessel functions present in the fundamental solutions. Particular attention is paid to the presence of domain loads, whose domain integral is transformed into a boundary one using the Radial Integral Method technique (RIM). These strategies lead to a robust procedure that allows obtaining good results even in the presence of boundary sparse discretization. This is demonstrated by the results of the examples carried out which, compared with the analytical solutions present in the literature, show a very good convergence.