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

The paper provides a state of the art review of guided wave based structural health monitoring (SHM). First, the fundamental concepts of guided wave propagation and its implementation for SHM is explained. Following sections present the different modeling schemes adopted, developments in the area of transducers for generation, and sensing of wave, signal processing and imaging technique, statistical and machine learning schemes for feature extraction. Next, a section is presented on the recent advancements in nonlinear guided wave for SHM. This is followed by section on Rayleigh and SH waves. Next is a section on real-life implementation of guided wave for industrial problems. The paper, though briefly talks about the early development for completeness,. is primarily focussed on the recent progress made in the last decade. The paper ends by discussing and highlighting the future directions and open areas of research in guided wave based SHM.

https://iopscience.iop.org/article/10.1088/0964-1726/25/5/053001/pdf

Guided wave based structural health monitoring: A review

Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution

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

Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature

A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates

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

Numerical and experimental investigations on the axial crushing response of composite tubes

In this article, two-scale 3D finite element (FE) models, the microscopic repeated unit cell (RUC) model for yarn, and mesoscopic-repeated unit cell model for woven composite, are presented to predict the effective stiffness properties of 3D woven orthogonal interlock composites. The micro-RUC model for the yarn is based on a hexagonal array of fibers. Undulation of the yarns in the novel 3-D meso-RUC for the woven composite is described by Hermit-spline function. The periodic boundary conditions are applied to the two-scale models during the 3D FE analysis in order to ensure that both the displacement and stress are continuous on the boundary surfaces. Specimens are manufactured with house-made resin transfer molding (RTM) equipment and simple tensile experiment is performed. It is found that the predicted yarn properties by the micro-RUC agree well with data computed by equations with a suitable parameter determined by experiment and the predicted effective stiffness properties of 3-D woven composites b...

https://imechanica.org/files/Periodicity%20boundary%20conditions.pdf

Multi-scale Analyses of 3D Woven Composite Based On Periodicity Boundary Conditions

In this paper a new version of Differential Quadrature Method (DQM) is proposed and then extended to analyse frame structures. The new method, called the Differential Quadrature Element Method (DQEM), retains all advantages of the earlier version of the differential quadrature method and overcomes some critical shortcomings existing in the original DQM. The proposed method is, however, different from the Quadrature Element Method (QEM) proposed earlier by Striz et al. The methodology is explained in details herein via a differential quadrature beam element and some numerical examples are given to show the efficiency of the present method. © 1997 by John Wiley & Sons, Ltd.

Xinwei Wang

Papers

A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates

Harmonic differential quadrature method and applications to analysis of structural components

Numerical and experimental investigations on the axial crushing response of composite tubes

Multi-scale Analyses of 3D Woven Composite Based On Periodicity Boundary Conditions

Static analysis of frame structures by the differential quadrature element method