Rectangular Plates Resting on Tensionless Elastic Foundation

Abstract

The behavior of elastic plates of rectangular shape on a tensionless Winkler foundation is analyzed. The tensionless character of the foundation is taken into account by using an auxiliary function. The displacement function of the plate is approximated by using the eigenfunctions of the completely free beam. The difference between the free‐end boundary conditions of the plate and the beam is compensated for by considering a differential operator in addition to the governing equation of the plate. Using Galerkin's method the problem is reduced to the solution of a system of algebraic equations. For various values of the external uniformly distributed load, concentrated load, and moment, the configurations of the contact curve and the displacement are given in figures.