Vibration and buckling calculations for rectangular plates subject to complicated in-plane stress distributions by using numerical integration in a rayleigh-ritz analysis

A Rayleigh-Ritz approach, in which appropriate beam characteristics functions are used in the deflection series, is presented for the solution of the elastic buckling and flexural vibration problems of thin rectangular plates which may be subject to any practical in-plane stress field. The stress distribution may be described in the form of mathematical expressions or by means of a set of values known only at discrete points within the plate; typically the former description may be derived from a classical two-dimensional elasticity solution and the latter from a finite difference or finite element analysis. The integrations associated with the in-plane stresses in the strain energy expression are performed numerically by using a technique based upon natural bicubic spline interpolation, the computer subroutines for which are available to the general scientific public. Several numerical examples of varying complexity are presented, illustrating the accuracy and applicability of the proposed approach.