New exact solutions for free vibrations of thin orthotropic rectangular plates

Xing, Yufeng; Liu, B.

doi:10.1016/j.compstruct.2008.11.010

Cited by 116 publications

(49 citation statements)

References 38 publications

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“…However, the applications of the DSC method to vibrations of plates are limited in straight-sided quadrilateral plates so far. It is noteworthy, recently, that some new exact solutions have been obtained by the present authors using direct separation of variables for rectangular plates with any combinations of simple support and clamp conditions [81,82].…”

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confidence: 94%

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

Xing

Liu

2009

Numerical Meth Engineering

131

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SUMMARYBased on the differential quadrature (DQ) rule, the Gauss Lobatto quadrature rule and the variational principle, a DQ finite element method (DQFEM) is proposed for the free vibration analysis of thin plates. The DQFEM is a highly accurate and rapidly converging approach, and is distinct from the differential quadrature element method (DQEM) and the quadrature element method (QEM) by employing the function values themselves in the trial function for the title problem.The DQFEM, without using shape functions, essentially combines the high accuracy of the differential quadrature method (DQM) with the generality of the standard finite element formulation, and has superior accuracy to the standard FEM and FDM, and superior efficiency to the p-version FEM and QEM in calculating the stiffness and mass matrices.By incorporating the reformulated DQ rules for general curvilinear quadrilaterals domains into the DQFEM, a curvilinear quadrilateral DQ finite plate element is also proposed. The inter-element compatibility conditions as well as multiple boundary conditions can be implemented, simply and conveniently as in FEM, through modifying the nodal parameters when required at boundary grid points using the DQ rules. Thus, the DQFEM is capable of constructing curvilinear quadrilateral elements with any degree of freedom and any order of inter-element compatibilities. A series of frequency comparisons of thin isotropic plates with irregular and regular planforms validate the performance of the DQFEM.

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confidence: 94%

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

Xing

Liu

2009

Numerical Meth Engineering

131

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“…Furthermore, Leissa et al [37] successfully presented exact solutions for vibration and buckling analysis of a SS-C-SS-C rectangular plate loaded by linearly varying in-plane stress, and later Kang et al [38] further extended that method to study the free vibration problem of laminated composites subjected to in-plane moments acting on two opposite simply supported edges. Recently, Xing and Liu [39] presented other new exact solutions for free vibration of thin orthotropic rectangular plates. In principle, exact solutions are desirable since they are capable of providing deep physical insight, more accurate and so forth.…”

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confidence: 99%

An efficient meshfree method for vibration analysis of laminated composite plates

2011

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A detailed analysis of natural frequencies of laminated composite plates using the meshfree moving Kriging interpolation method is presented. The present formulation is based on the classical plate theory while the moving Kriging interpolation satisfying the delta property is employed to construct the shape functions. Since the advantage of the interpolation functions, the method is more convenient and no special techniques are needed in enforcing the essential boundary conditions. Numerical examples with different shapes of plates are presented and the achieved results are compared with reference solutions available in the literature. Several aspects of the model involving relevant parameters, fiber orientations, lay-up number, length-to-length, stiffness ratios, etc. affected on frequency are analyzed numerically in details. The convergence of the method on the natural frequency is also given. As a consequence, the applicability and the effectiveness of the present method for accurately computing natural frequencies of generally shaped laminates are demonstrated.

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“…(9) and (10) above are obtained, the classical method to carry out an exact buckling analysis of a plate consists of (i) solving the system of differential equations in Navier or Lèvy-type closed form in an exact manner, (ii) applying particular boundary conditions on the edges and finally (iii) obtaining the stability equation by eliminating the integration constants [41,42,43,44]. This method, although extremely useful for analysing an individual plate, it lacks generality and cannot be easily applied to complex structures assembled from plates for which researchers usually resort to approximate methods such as the FEM.…”

Section: Dynamic Stiffness Formulationmentioning

confidence: 99%

Buckling of composite plate assemblies using higher order shear deformation theory—An exact method of solution

Fazzolari

Banerjee

Boscolo

2013

Thin-Walled Structures

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Citation: Fazzolari, F. A., Banerjee, J. R. and Boscolo, M. (2013). Buckling of composite plate assemblies using higher order shear deformation theory-An exact method of solution. Thin-Walled Structures, 71, pp. 18-34. doi: 10.1016/j.tws.2013 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractAn exact dynamic stiffness element based on higher order shear deformation theory and extensive use of symbolic algebra is developed for the first time to carry out a buckling analysis of composite plate assemblies. The principle of minimum potential energy is applied to derive the governing differential equations and natural boundary conditions. Then by imposing the geometric boundary conditions in algebraic form the dynamic stiffness matrix, which includes contributions from both stiffness and initial pre-stress terms, is developed. The Wittrick-Williams algorithm is used as solution technique to compute the critical buckling loads and mode shapes for a range of laminated composite plates including stiffened plates. The effects of significant parameters such as thickness-to-length ratio, orthotropy ratio, number of layers, lay-up and stacking sequence and boundary conditions on the critical buckling loads and mode shapes are investigated. The accuracy of the method is demonstrated by comparing results whenever possible with those available in the literature.

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New exact solutions for free vibrations of thin orthotropic rectangular plates

Cited by 116 publications

References 38 publications

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

An efficient meshfree method for vibration analysis of laminated composite plates

Buckling of composite plate assemblies using higher order shear deformation theory—An exact method of solution

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