Differential Quadrature Method in Computational Mechanics: A Review

Abstract

The differential quadrature method is a numerical solution technique for initial and/or boundary problems. It was developed by the late Richard Bellman and his associates in the early 70s and, since then, the technique has been successfully employed in a variety of problems in engineering and physical sciences. The method has been projected by its proponents as a potential alternative to the conventional numerical solution techniques such as the finite difference and finite element methods. This paper presents a state-of-the-art review of the differential quadrature method, which should be of general interest to the computational mechanics community.

Free vibrations of non-uniform CNT/fiber/polymer nanocomposite beams

“…GDQ technique, as an efficient numerical technique, is implemented for solving partial differential equations, especially in the field of solid mechanics [37][38][39][40][41]. Here, this method is utilized to obtain the natural frequencies of non-uniform CNTFPC beam.…”

The Effect of Residual Stress on the Electromechanical Behavior of Electrostatic Microactuators

“…, N, are selected, the coefficients of the differential quadrature weighting matrix can be obtained from (4). Higher order derivatives of the differential quadrature weighting coefficients can also be directly calculated by matrix multiplication [34], which can be expressed as…”

“…The selection of sample points is important for the accuracy of the differential quadrature method solution, but inaccurate results have been obtained when using this uniform distribution. A nonuniform sample point distribution, such as the Chebyshev-Gauss-Lobatto distribution [34], improves the accuracy of the calculation. The integrity and computational efficiency of the differential quadrature method in solving this problem will be demonstrated using a set of case studies.…”

An Improved Differential Quadrature Time Element Method

“…The basic idea of DQ rule is to analogously obtain the derivative of a function or variable by a weighted linear sum of the function or variable values at all discrete points in the domain [41,42], the r-th derivatives of f (x) at the i-th point can be expressed by…”