Some fundamental solutions for the Kirchhoff, Reissner and Mindlin plates and a unified BEM formulation

We derive analytical solutions for the deflection of thin circular plates, which are loaded by centrally located concentrated bending moments and tran sverse forces. Green's functions for clamped and simply supported plates ar e presented. Reduction of these Green's functions leads to the correspondin g fundamental solution for the Kirchhoff plate bending model (K problem). T his fundamental solution reduces to those obtained through the direct simpl ification of the fundamental solution for the sixth-order Reissner and Mind lin plate bending models (RM problem). This allows to decompose each fundam ental tensor of the problem RM into the sum of the fundamental tensor of th e problem K and a correction tensor (Sh problem), which contains the contri bution of the shear strains, e.g. U-ij(RM)(r) = U-ij(K)(r) + U-if(Sh)(r). W ithin the boundary element analysis this enables the investigation of the c ontributions of the shear strains to the solutions of Reissner and Mindlin plate bending models, as corrections of the Kirchhoff values, all determine d from the same BEM code. This opens up new possibilities for the analysis of plates by the BEM. (C) 2001 Elsevier Science Ltd. All rights reserved.