A generalized differential quadrature rule for bending analysis of cylindrical barrel shells

Abstract

The generalized differential quadrature rule (GDQR) proposed recently by the present authors is applied here to solve an eighth-order boundary-value differential equation with four boundary conditions at each boundary, which governs the bending analysis of circular cylindrical barrel shells. Thus, multiple boundary conditions are implemented exactly at boundaries without applying the approximate δ-point (non-boundary point) technique. Both Hermite interpolation functions and GDQR’s explicit weighting coefficients are obtained, while the latter are the most important for an accurate implementation of the GDQR. The analytical results for various cylindrical barrel shells are derived and calculated here in order to verify the accuracy of the calculated GDQR results. In implementation of multiple conditions at one point, the GDQR gains a clear advantage over the existing δ-point technique in the differential quadrature applications and manifests a great potential for applications in many fields of applied mathematics.