The generalized differential quadrature rule for fourth-order differentialequations

The generalized differential quadrature rule (GDQR) proposed here is aimed at solving high-order differential equations. The improved approach is comp letely exempted from the use of the existing delta -point technique by appl ying multiple conditions in a rigorous manner. The GDQR is used here to sta tic and dynamic analyses of Bernoulli-Euler beams and classical rectangular plates. Numerical error analysis caused by the method itself is carried ou t in the beam analysis. Independent variables for the plate are first defin ed. The explicit weighting coefficients are derived for a fourth-order diff erential equation with two conditions at two different points. It is quite evident that the GDQR expressions and weighting coefficients for two-dimens ional problems are not a direct application of those for one-dimensional pr oblems. The GDQR are implemented through a number of examples. Good results are obtained in this work. Copyright (C) 2001 John Wiley & Sons, Ltd.