Keywords: differential quadrature, extended differential quadrature, differential quadrature element method, differential quadrature finite difference method, time-element by time-element method, stages by stages method.

The author has generalized and extended DQ method which results in obtaining the generic differential quadrature (GDQ) method and the extended differential quadrature (EDQ) method. The weighting coe.cients for a grid model having an arbitrary configuration defined by a coordinate system having arbitrary dimensions can also be generated. A certain order derivative or partial derivative of the variable function with respect to the coordinate variables at a discrete point, which might not be a node, is expressed as the weighted linear sum of the values of function and/or its possible derivatives or partial derivatives at all nodes. The time variable can also be a coordinate variable. Consequently, not only the spacial discretization but also the temporal discretization can be carried out by using GDQ and EDQ. Time integration algorithms by using these techniques for transient analyses have also been developed.

The author has also used DQ, GDQ and EDQ to develop the discrete element analysis methods differential quadrature element method (DQEM), generalized differential quadrature element method (GDQEM), differential quadrature finite difference method (DQFDM) and differential quadrature finite element method (DQFEM) for solving a generic, linear or nonlinear, steady-state or transient, composite structural problem having an arbitrary domain configuration. In this paper, numerical procedures for calculating various weighting coe.cients and generating weighting coe.cients of EDQ by using the DQ weighting coefficients are summarized and presented. Numerical results of some sample problems solved by using the developed numerical methods are also presented.

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