A new unconstrained third-order plate theory for Navier solutions of symmetrically laminated plates

Leung, A.Y.T.; Niu, Junchuan; Lim, C.W.; Song, Kaidi

doi:10.1016/s0045-7949(03)00290-6

Cited by 27 publications

(8 citation statements)

References 20 publications

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“…Therefore, Leung's theory is particularly useful for the study of a plate with contact friction or present in a flow field where the boundary layer shear stress is significant. The differences of the two theories are, additionally, so small that they cannot be easily found in the below simulation figures, but Leung's theory with similar complexity as Reddy's theory yields more accurate solutions in comparison with the exact three-dimensional solutions [24]. For the unconstrained third-order beam model [22][23][24], the displacement field for a beam on the x-y plane is expressed as…”

Section: Displacement Fields and The Governing Equationsmentioning

confidence: 99%

“…This article presents formulations of non-local third-order nanobeam theories for bending, buckling, and vibration of nanobeams via the variational principle based on Eringen's non-local theory and Reddy [20,21] and Leung [22][23][24] higher-order beam models. An asymptotic governing differential equation of infinite-order strain gradients is derived.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Third-order non-local beam theories for the analysis of symmetrical nanobeams

Niu

Lim

Leung

2009

Proceedings of the Institution of Mechanical Engineers, Part C:

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This article presents formulation of third-order non-local beam theories based on Eringen's non-local continuum theory and the Reddy and Leung higher-order beam models for bending, buckling, and vibration of nanobeams. By applying the variational principle, an asymptotic governing differential equation of infinite-order strain gradients is derived and subsequently the governing equation of motion of the nanobeams is obtained. For practical applications, the Navier solutions of the asymptotic non-local model are presented and discussed. Bending, buckling, and vibration of nanobeams with simply supported boundary conditions are investigated. Numerical examples are presented to illustrate the corresponding effects of non-local scale parameter, rotary inertia and transverse shear deformation on deflections, buckling loads, and natural frequencies of nanobeams.

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Section: Displacement Fields and The Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Third-order non-local beam theories for the analysis of symmetrical nanobeams

Niu

Lim

Leung

2009

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…The differential equations for UTSDT are of similar complexity to those of TSDT. This approach produces more accurate solutions [33]. Responses of the laminated plates using UTSDT were also investigated in [33].…”

Section: Introductionmentioning

confidence: 99%

“…This approach produces more accurate solutions [33]. Responses of the laminated plates using UTSDT were also investigated in [33]. Static and free vibration analyses of composite plates using radial point interpolation method (RPIM) combined with UTSDT were reported in [34].…”

Section: Introductionmentioning

confidence: 99%

An efficient computational approach for control of nonlinear transient responses of smart piezoelectric composite plates

Phung‐Van¹,

Nguyen²,

Tran³

et al. 2015

International Journal of Non-Linear Mechanics

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ABSTRACTAn efficient computational approach based on a generalized unconstrained approach in conjunction with isogeometric analysis (IGA) are proposed for dynamic control of smart piezoelectric composite plates. In composite plates, the mechanical displacement field is approximated according to the proposal model using isogeometric elements and the nonlinear transient formulation for plates is formed in the total Lagrange approach based on the von Kármán strains and solved by Newmark time integration. Through the thickness of each piezoelectric layer, the electric potential is assumed linearly.For active control of the piezoelectric composite plates, a close-loop system is used. An optimization procedure using genetic algorithm (GA) is considered to search optimal design for actuator input voltages. Various numerical examples are investigated to show high accuracy and reliability of the proposed method.

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“…Further, Reddy and Wang [13] discussed an overview of algebraic relationships between solutions of CPT and those of FOST and TOT plate theories of FG plates. Leung et al [14] discussed TOT in study of laminated plates . Transverse shear stresses on top and bottom plate surface are vanishing, and results are compared with CPT and FOST. Zenkour [15] presented static response for a simply supported FG rectangular plate subjected to a transverse uniform load.…”

Section: Introductionmentioning

confidence: 99%