Buckling and free vibration of moderately thick square plates using coupled displacement field method

Abstract

A simple and efficient coupled displacement field method is developed to study the buckling load and fundamental frequency parameters of the moderately thick square plates. A single term trigonometric admissible displacement field is assumed for one of the variables, say, the total rotations (in both X, Y directions). Making use of the coupling equation, the spatial variation for the lateral displacement field is derived in terms of the total rotations. The coupled displacement field method makes the energy formulation to contain half the number of unknown independent coefficients, in the case of a square plate, contrary to the conventional Rayleigh-Ritz method. The lesser number of undetermined coefficients significantly simplifies the buckling and free vibration analyses. The expressions for the non-dimensional buckling load and fundamental frequency parameters of the moderately thick square plates with all the edges simply supported and clamped are derived. The numerical values of these parameters obtained using the coupled displacement field method and the Rayleigh-Ritz method match very well demonstrating the effectiveness of the coupled displacement field method.