Analysis of Circular Elastic Plate Resting on Pasternak Foundation by Strain Energy Approach

Abstract

In this paper, an analytical expression for the deflection of a thin circular elastic plate resting on the Pasternak foundation is derived by adopting the strain energy approach. The parametric study is carried out to observe the location of the plate lift-off and the variation of the deflection profiles for comparing the variation pattern reported in the literature based on an approximate solution technique. It is found that the radial distance of the point of lift-off of the plate decreases with increase in the values of both the shear modulus and the modulus of subgrade reaction of the foundation soil; the reduction being more for their lower values. It is also observed that the variation in deflection of the plate at any radial distance due to change in soil subgrade conditions is significant for lower values of modulus of subgrade reaction

On the transient response of plates on fractionally damped viscoelastic foundation

“…Huang et al (2008) presented the analytical solution of a functionally-graded plate resting on the Winkler-Pasternak elastic foundation, using the three-dimensional theory of elasticity. Shukla et al (2011) studied the static response of a thin circular plate resting on the two-parameter Pasternak foundation, subjected to a concentrated load using the strain energy approach. The damping of the foundation was neglected with these elastic foundation models.…”

Untitled

“…A full-field solution is obtained therein by means of the Wiener-Hopf method and the influence of the subgrade parameters on the stress intensity factors at the crack tip are evaluated in detail. Recently, Shukla et al [2011] have obtained the solution of a circular plate supported by a tensionless Pasternak-type subgrade by using the strain energy approach and assuming a power series expansion for the transverse deflection of the plate. Variational boundary conditions for a beam resting on a twoparameter tensionless elastic foundation have been developed in [Nobili 2012].…”