Strain energy analysis of rectangular plates resting on elastic foundation and fundamental study on validity and applicable range of first-order shear deformation theory

Abstract

This paper presents a strain energy analysis of four edges simply supported rectangular plates resting on elastic foundation. The analysis is based on the three-dimensional (3-D) theory of elasticity, and the elastic foundation is described by the Winkler model. An analytical solution was exactly derived by using the double Fourier series expansions. The effects of thickness-to-length ratio, aspect ratio, non-dimensional foundation parameter and transeverse load on the strain energy and elastic energy of rectangular plates resting on elastic foundation are investigated in detail. Moreover, the validity and applicable range of the first-order shear deformation theory, called Mindlin plate theory, in comparison with 3-D analysis were also presented for bending problem of rectangular plates under transeverse load on elastic foundation.