A Variational Approach for the Analysis of Square and Rectangular Plates Resting in Smooth Contact with an Isotropic Elastic Halfspace

Abstract

ABSTRACT Flexures of thin square and rectangular plates resting in smooth contact with a linearly deformable elastic halfspace are examined using a variational approach. The plates may be subjected to uniformly distributed loads and/or symmetrically located concentrated loads. Deflected shape of the plate is assumed as a polynominal in terms of the spatial coordinates x and y. The contact stress distribution at the plate-elastic halfspace interface is then expressed as a direct function of the assumed plate deflection, where stress singularity at the edges is taken into account. Numerical results are obtained for plate deflections, flexural moments and contact stress distributions for various plate rigidities. Comparison of results with the existing equivalent solutions shows that the proposed analysis technique yields reasonably accurate resuts for a wide range of plate rigidities.