The generalized differential quadrature rule for fourth-order differential equations

Abstract

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