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.

Differential Quadrature Method in Computational Mechanics: A Review

Numerical Methods for Scientists and Engineers

Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey

https://espace.library.uq.edu.au/view/UQ:415632/UQ415632_OA.pdf

Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams

2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures

Two approximate methods, which have not previously been used for structural dynamics problems, are applied to the free vibration analysis of various structural components. The first method is a new version of the complementary energy method. It is shown to be considerably more accurate than the conventional Rayleigh and Rayleigh-Schmidt methods when applied to spatially one-dimensional free vibration problems: prismatic and tapered bars, prismatic beams, and axisymmetric motion of circular membranes. The second method is the differential quadrature method introduced by Bellman and his associates. It is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates.

Two new approximate methods for analyzing free vibration of structural components

The numerical technique of differential quadrature for the solution of linear and non-linear partial differential equations, first introduced by Bellman and his associates, is applied to the equations governing the deflection and buckling behaviour of one- and two-dimensional structural components. Separate transformations are used for higher-order derivatives, as suggested by Mingle, thus extending the method to treat fourth-order equations and to include multiple, boundary conditions in the respective co-ordinate directions. Results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods. The application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computational effort.

Application of differential quadrature to static analysis of structural components

Differential quadrature for static and free vibration analyses of anisotropic plates

Static analysis of structures by the quadrature element method(QEM)

The behavior of thin, circular, isotropic elastic plates with immovable edges and undergoing large deflections is investigated by the numerical technique of differential quadrature. Approximate results are determined with the aid of a symbolic manipulation computer program and a Newton-Raphson technique to solve the nonlinear systems of equations. Bending stresses, membrane stresses, and deflections are calculated for clamped and simply supported flexural edge conditions and for a uniform pressure load and a concentrated load at the center.

Alfred G. Striz

Papers

Two new approximate methods for analyzing free vibration of structural components

Application of differential quadrature to static analysis of structural components

Differential quadrature for static and free vibration analyses of anisotropic plates

Static analysis of structures by the quadrature element method(QEM)

Nonlinear bending analysis of thin circular plates by differential quadrature