Structural analysis of rectiliner flat plates of arbitrary plan forms by boundary integral method

Abstract

The boundary integral method for the solution of rectilinear thin isotropic elastic plates of arbitrary plan forms subjected to transverse forces is presented. The direct formulation which makes use of Betti’s reciprocal theorem based on energy consideration is employed to solve the problems with interior supports in the plate domain. Included herein are the axial and rotational stiffness of interior supports. The proposed formulation leads to a system of boundary integral equations involving displacement, normal slope, normal bending moment and supplemented shear on the boundary. The handling of interior supports is that the usual boundary equations have to be supplemented by three additional conditions for each supports. Thereafter, a numerical scheme of computation is used to solve the resulting integral equations approximately by simple discretization of the boundary functions. Treatment of singularities is also discussed in detail. Some numerical results are given in illustrative curves. They are found to be in fairly good agreement with those of other current investigators and with the finite element solution. A computer program is developed for the method proposed to give results with practical accuracy in this study.