Spline-based differential quadrature for fourth order differential equations and its application to Kirchhoff plates

摘要

A quintic B-spline-based differential quadrature method (SDQM) is developed to deal with fourth order differential equations. With the construction of cardinal spline interpolations using the normalized quintic B-spline functions, explicit expressions of weighting coefficients for approximation of derivatives are obtained. Some bending, buckling problems of the Kirchhoff plate characterized by fourth order differential equations are studied using the method. Very good agreement with other available solutions is reached. Numerical results show that the newly constructed spline-based differential quadrature is more versatile than the conventional differential quadrature. The present spline-based differential quadrature is found to be an effective alternative to the conventional differential quadrature.