Approximate three-dimensional analysis of rectangular thick laminated plates: Bending, vibration and buckling

Abstract

A global-local approach is proposed to analyse thick laminated plates. This approach treats a thick laminated plate as a three-dimensional inhomogeneous anisotropic elastic body. The cross-section of a laminated plate is first discretized into conventional eight-node elements. The interpolation function along the span of the plate is defined by the cubic B 3-spline function. The displacement functions can be expressed as the product of the usual isoparametric shape functions and the spline function. A set of global polynomials of an appropriate order is selected to transform the nodal variables of the cross-section to a much smaller set of generalized parameters associated with the polynomials. These parameters can be obtained by means of the standard Rayleigh-Ritz technique. The total number of unknowns involved is drastically reduced with a minor sacrifice of accuracy. The six components of stresses, the fundamental natural frequencies and the critical buckling loads can be determined with acceptable accuracy. Numerical examples are given to demonstrate the accuracy and effectiveness of the global-local procedures.