Large deflection response of annular plates on Pasternak foundations

Abstract

The influence of the elastic foundation configuration on the large deflection axisymmetric response of cylindrically orthotropic thin annular plates is examined for uniformly distributed loads. The solution of the dynamic form of the Von Kármán type equations governing the behaviour of the system is obtained using a fourth order finite difference representation for the spatial domain with the Newmark-β scheme being used for the time domain. Results for the fixed edge and simply supported immovable edge boundary conditions for a plate on a Pasternak foundation with or without an annular cut-out are presented for both the static and step loading cases. The inner edge boundary conditions for these configurations of a Pasternak foundation are examined and the apparent anomaly of the annular foundation increasing the stiffness in the recent literature addressed. The significance of the foundation parameters on plate response as well as the geometric non-linearity is considered.