Rectangular anisotropic (orthotropic) plates on a tensionless elastic foundation

Abstract

The behavior of anisotropic (orthotropic) elastic plates of rectangular shape on a tensionless Winkler foundation is analyzed. The tensionless character of the foundation is taken into account by suing an auxiliary function. The displacement function of the plate is approximated 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. The governing equations of the plate are derived under action of external uniformly distributed load, concentrated load, and moments. However, the influence of the mechanical properties on the configurations of the contact region and on the distribution of the displacements is investigated for concentrated load and moments for various values of the the mechanical properties characterizing the anisotropy of the plate material. Considered problems are solved within the framework of Kirchhoff-Love hypothesis.