Plates on Biparametric Elastic Foundation by BDIE Method

Abstract

An efficient boundary differential integral equation (BDIE) method is presented for the analysis of thin elastic plates with free boundaries of any shape resting on biparametric elastic foundation. The plate, which may have holes, is subjected to concentrated loads, line loads, or distributed surface loads. The solution is achieved by converting the governing boundary value problem to an equivalent problem consisting of five coupled boundary equations, two of which are differential and three of which are integral. The boundary differential equations are derived from the boundary conditions, while the boundary integral equations are derived from the integral representations for the deflections of the plate and of the foundation region. A numerical technique based on the discretization of the boundary is developed for the solution of the boundary equations. The computational efficiency of the method is increased by converting the domain integrals attributable to loading into boundary line integrals. Numerical results for several plates are obtained to attest to and demonstrate the accuracy and the efficiency of the presented BDIE method.