Shear deformable plate subjected to internal distortion by SGBEM

Abstract

The Symmetric Galerkin Boundary Element Method (SGBEM) is applied to shear deformable plates of Mindlin's type subjected to internal distortion. In the present paper, the domain integral with strong or hypersingular kernel, pertaining to constant internal distortion, are transformed in boundary ones. In the Somigliana's Identity (S.I) of deformations, the domain integral presents a hypersingular kernel. This integral is subject to a regularization process, which makes it possible to divide it into two parts. The first part is evaluated as Cauchy Principal Value and divided into a regular part and a singular part; the latter is transformed into boundary integral using the Radial Integral Method (R.I.M). The second part of the original integral is transformed, using Gauss's theorem, in order to obtain a matrix of free domain terms called Bui Free Terms. These operations make it possible to replace the hyper-singular integral of the S.I. of the deformations with a boundary one to which a constant term is added. The expressions thus obtained for the displacements and tractions are utilized for the evaluation of the load coefficient connected to internal distortion. This strategy make it possible to evaluate the load coefficients avoiding considerable difficulties due to the geometry of the analyzed solid.