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Trigonometric solution for an exponentially graded thick plate resting on elastic foundations

Zenkour A. M.

Archive of Mechanical Engineering

2018

Vol. LXV, nr 2

193--208

This article investigates the solution of exponentially graded (EG) thick rectangular plates resting on two-parameter elastic foundations according to a trigonometric plate theory (TPT). This theory includes the eﬀect of both shear and normal strains thickness without needing to any shear correction factor. The displacement ﬁelds contains initial terms of a power series across plate thickness as well as additional trigonometric terms. The material properties of plate is graded such that Lamé’s coeﬃcients convert exponentially in a given constant orientation.Equilibrium equations according to the EG plate resting on Pasternak’s foundations are derived. The solution is obtained by using Navier’s technique. Numerical results for the EG thick plate on elastic foundations are presented, and compared with those available in the literature. The inﬂuences of Winkler’s and Pasternak’s parameters, side-to-thickness ratio, inhomogeneity parameter and aspect ratio on the bending responses of EG plates are investigated.