A new differential quadrature methodology for beam analysis and the associated differential quadrature element method

Abstract

This paper presents a computationally efficient and an accurate new methodology in differential quadrature analysis of beam elements. The methodology would overcome the difficulties in boundary conditions implementations of fourth-order differential equations encountered in such problems. The methodology benefited from defining the second-order derivatives along the boundaries as independent degrees of freedom would enable the differential quadrature method to exactly satisfy some types of boundary conditions; where by most other conventional algorithms have to be satisfied approximately. The weighting coefficients employed are not exclusive, and any accurate and efficient method such as the generalized differential quadrature method may be used to produce the methods weighting coefficients. By solving some typical stability, deflection and frequency analysis beam problems and by comparing the results with those of exact solutions and/or those of other methodologies, accuracy, convergency and efficiency of the methodology is asserted. In order to generalize its application to large-scale beam structures and to the cases with the discontinuity in loading conditions and geometry, a new one-dimensional differential quadrature element method formulation is presented and implemented.