Pb-2 Rayleigh - Ritz method for general plate analysis

Abstract

An alternative method to the widely used finite element method for elastic analysis of thin plates, the pb-2 Rayleigh - Ritz method, is presented. The special feature of the pb-2 Rayleigh - Ritz method lies in the definition of the Ritz functions which consist of the product of a basic function and a two-dimensional polynomial function where the number of terms may be increased until the desired accuracy is achieved. The basic function is formed by the product of all the boundary equations; each of which is raised to the power of either 0, 1 or 2, corresponding to either free, simply supported or clamped edges, respectively. Thus the basic function ensures the satisfaction of the kinematic boundary conditions at the outset. The bending, buckling and vibration analyses are presented in a unified form and the pb-2 Rayleigh - Ritz method is applied to solve some plate examples to illustrate its simplicity and accuracy.