Bending analysis of orthotropic thin plate on graded elastic foundation

Based on the energy method and variation principle, the bending analysis is presented for orthotropic thin plates on graded elastic foundations subjected to distributed loads using two-parameter foundation model. Firstly, the bending differential equilibrium equation of orthotropic thin plates on graded elastic foundations and the expressions of two elastic parameters of elastic foundation are given by introducing the energy method and variation principle. Then, the displacement reduced function φ(z) is derived based on the assumption that the normal stress in z-direction is uniform through foundation thickness. In the example, the proposed solution is validated by comparing the degenerated results for homogeneous isotropic foundation with Vlazov model. Finally, this paper studies the displacements distributions of the orthotropic thin plate on a graded elastic foundation, whose Young's modulus obeys a power law through the thickness. The effects of top-bottom surfaces' Young's modulus ratio λ and volume fraction exponent n on the variation of deflection of the plate are also examined.