Differential quadrature: a powerful new technique for analysis of composite structures

Bert, Charles W.; Malik, M.

doi:10.1016/s0263-8223(97)00112-8

Cited by 149 publications

(57 citation statements)

References 39 publications

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“…Kong and Cheung [58] discussed a "nite layer method on free vibration. Bert and Malik [30] analyzed laminated composite structures using the di!erential quadrature numerical method based on the "rst order shear deformation theory with a shear correction factor /12. For a thick plate of up to a/h"5, it is unlikely for the transverse displacement to vary through thickness as regular plates.…”

Section: E+ect Of Orthotropy-thick Laminatesmentioning

confidence: 99%

Comparison of Natural Frequencies of Laminates by 3-D Theory, Part I: Rectangular Plates

Chao

Chern

2000

Journal of Sound and Vibration

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Section: E+ect Of Orthotropy-thick Laminatesmentioning

confidence: 99%

Comparison of Natural Frequencies of Laminates by 3-D Theory, Part I: Rectangular Plates

Chao

Chern

2000

Journal of Sound and Vibration

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“…Postulating smooth function f(x,y) in the region 0 ≤ x ≤ a, 0 ≤ y ≤ b, the r-th order partial derivative of f(x,y) with respect to x, the s-th order partial derivative of f(x,y) with respect to y and the mixed partial derivative of the s-th order with respect to y and the r-th order with respect to x are respectively approximated as [35] where N, M is the number of grid points in the x and y direction, respectively, and are the weighted coefficients, and they are defined by…”

Section: Dynamic Characteristics and Stability Of Axially Moving Viscmentioning

confidence: 99%

Dynamic Characteristics and Stability of Axially Moving Viscoelastic Plate with Piezoelectric Layer

Wang

Cao

Tao

et al. 2014

Journal of Low Frequency Noise, Vibration and Active Control

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The dynamic stability of the moving viscoelastic plate with the piezoelectric layer is studied. On the basis of the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of the axially moving viscoelastic rectangular plate with piezoelectric layer in the Laplace domain is formulated, the equation is suitable for various viscoelastic differential models. Then, the differential equation of motion of the viscoelastic plate with elastic dilatation and Kelvin-Voigt distortion in time domain is derived, with the piezoelectric effect. The complex eigenvalue equations of axially moving viscoelastic plate are established by the differential quadrature method. The generalized eigenvalue equations are solved, and the force excited by the piezoelectric layer due to external voltage is modeled as the follower tensile force; this force is used to improve the stability of the axially moving viscoelastic plate. Via numerical calculation, the results for the instability type and the corresponding critical moving speed of viscoelastic plate are presented to show the variations in these factors with respect to the dimensionless moving speed, the dimensionless delay time and the applied voltages. The dynamic stability of the axially moving viscoelastic plates can be effectively improved by the determination of the optimal location for the piezoelectric layers and the most favorable voltage assignment.

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“…The collocation method is ideal in application to structural theories and has found several instances in the scientific literature [9]. With reference to the analysis of shell structural elements, Mirfakhraei and Redekop [10] applied a Lagrangian differential quadrature method to the study of buckling phenomena of orthotropic thin shells of revolution; Wu et al [11,12] presented solutions to problems of axisymmetric bending of shells of revolution, introducing the so-called generalized differential quadrature rule.…”

Section: Introductionmentioning

confidence: 99%

NURBS-Based Collocation Methods for the Structural Analysis of Shells of Revolution

Bellis

Artioli

2016

Metals

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Abstract:In this work we present a collocation method for the structural analysis of shells of revolution based on Non-Uniform Rational B-Spline (NURBS) interpolation. The method is based on the strong formulation of the equilibrium equations according to Reissner-Mindlin theory, with Fourier series expansion of dependent variables, which makes the problem 1D. Several numerical tests validate convergence, accuracy, and robustness of the proposed methodology, and its feasibility as a tool for the analysis and design of complex shell structures.

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Differential quadrature: a powerful new technique for analysis of composite structures

Cited by 149 publications

References 39 publications

Comparison of Natural Frequencies of Laminates by 3-D Theory, Part I: Rectangular Plates

Comparison of Natural Frequencies of Laminates by 3-D Theory, Part I: Rectangular Plates

Dynamic Characteristics and Stability of Axially Moving Viscoelastic Plate with Piezoelectric Layer

NURBS-Based Collocation Methods for the Structural Analysis of Shells of Revolution

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