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

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

Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns

Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method

Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates

The behavior of thin, rectangular, orthotropic elastic plates, with immovable edges and undergoing large deflections, is investigated by the numerical technique of differential quadrature. Approximate results are obtained, using the Newton-Raphson method and, alternatively, a finite-difference-based method to solve the nonlinear systems of equations. Bending stresses, membrane stresses, and deflections are calculated for plates with fully clamped and simply supported flexural edge conditions under uniform pressure loading. Results are compared with existing analytical, numerical, and experimental ones. The present method gives good accuracy and is computationally efficient.

Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature

A harmonic differential quadrature (HDQ) method with application to the analysis of buckling and free vibration of beams and rectangular plates is presented A new approach is proposed for the determination of the weighting coefficients for differential quadrature It is found that the HDQ method is more efficient than the ordinary differential quadrature (DQ) method, especially for higher order frequencies and for buckling loads of rectangular plates under a wide range of aspect ratios Also, some shortcomings existing in theDQ method are removed

Harmonic differential quadrature method and applications to analysis of structural components

The new approach for application of boundary conditions in the differential quadrature (DQ) method, proposed earlier by the present authors, is extended to generalized force boundary conditions in two dimensions A variety of problems is then analyzed by theDQ method with the new approach for application of boundary conditions, such as deflections of beams and circular and rectangular plates under nonuniformly distributed loadings, deflection of a rectangular plate on a Winkler foundation, and buckling and free vibrational analyses of circular plates It is found that the present method gives good accuracy and is computationally efficient Exact solutions can be obtained by theDQ method if analytical solutions are polynomials and the method is insensitive to the spacing of grid points for the cases considered

A. G. Striz

Papers

Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature

Harmonic differential quadrature method and applications to analysis of structural components

Static and free vibrational analysis of beams and plates by differential quadrature method