Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading

Ma, Liang; Lee, D.W.

doi:10.1016/j.euromechsol.2011.06.016

Cited by 112 publications

(36 citation statements)

References 21 publications

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“…The nonlinear thermal dynamic buckling of FG beams is also investigated by Ghiasian et al [29]. Ma and Lee [30] proposed exact solutions for nonlinear bending behaviour of FG beams under an in-plane thermal loading. Malekzadeh and Monajjemzadeh [31] investigated the dynamic thermal response of FG beams under a moving load.…”

Section: Introductionmentioning

confidence: 99%

Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams

Nguyen

et al. 2017

Composite Structures

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Northumbria University has developed Northumbria Research Link (NRL) to enable users to access the University's research output. Copyright © and moral rights for items on NRL are retained by the individual author(s) and/or other copyright owners. Single copies of full items can be reproduced, displayed or performed, and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided the authors, title and full bibliographic details are given, as well as a hyperlink and/or URL to the original metadata page. The content must not be changed in any way. Full items must not be sold commercially in any format or medium without formal permission of the copyright holder. The full policy is available online: http://nrl.northumbria.ac.uk/policies.html This document may differ from the final, published version of the research and has been made available online in accordance with publisher policies. To read and/or cite from the published version of the research, please visit the publisher's website (a subscription may be required.)Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams AbstractThe hygro-thermal effects on vibration and buckling analysis of functionally graded beams are presented in this paper. The present work is based on a higher-order shear deformation theory which accounts for a hyperbolic distribution of transverse shear stress and higher-order variation of in-plane and out-of-plane displacements. Equations of motion are obtained from Lagrange's equations. Ritz solution method is used to solve problems with different boundary conditions. Numerical results for natural frequencies and critical buckling temperatures of functionally graded beams are compared with those obtained from previous works. Effects of power-law index, span-to-depth ratio, transverse normal strain, temperature and moisture changes on the results are discussed.

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Section: Introductionmentioning

confidence: 99%

Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams

Nguyen

et al. 2017

Composite Structures

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“…It is reported that the effect of applied actuator smart layers is somehow negligible on thermal buckling control. In an analytical study, Ma and Wang [18] analyzed the nonlinear response of FGM beams with shear deformation effects and obtained the exact closed-form solutions for equilibrium path of the beam. This analytical study also proves the importance of the boundary conditions on the beam equilibrium path.…”

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confidence: 99%

Thermomechanical buckling oftemperature-dependent FGM beams

Kiani

Eslami

2013

Lat. Am. j. solids struct.

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“…Our formulae are based on the geometric middle surface. However, they can be easily shown to be equivalent to the formulae provided in [26,27] which are based on the physical neutral plane of the FGM structures. The terms N T and M T in (2.10) are the thermal stress resultants and moment caused by the temperature field.…”

Section: Basic Equationsmentioning

confidence: 99%

Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam

Meguid

et al. 2014

Proc. R. Soc. A.

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In this paper, we provide a unified and selfconsistent treatment of a functionally graded material (FGM) microbeam with varying thermal conductivity subjected to non-uniform or uniform temperature field. Specifically, it is our objective to determine the effect of the microscopic size of the beam, the electrostatic gap, the temperature field and material property on the pull-in voltage of the microbeam under different boundary conditions. The nonuniform temperature field is obtained by integrating the steady-state heat conduction equation. The governing equations account for the microbeam size by introducing an internal material length-scale parameter that is based on the modified couple stress theory. Furthermore, it takes into account Casimir and van der Waals forces, and the associated electrostatic force with the first-order fringing field effects. The resulting nonlinear differential equations were converted to a coupled system of algebraic equations using the differential quadrature method. The outcome of our work shows the dramatic effect and dependence of the pull-in voltage of the FGM microbeam upon the temperature field, its gradient for a given boundary condition. Specifically, both uniform and non-uniform thermal loading can actuate the FGM microbeam even without an applied voltage. Our work also reveals that the non-uniform temperature field is more effective than the uniform temperature field in actuating a FGM cantilever-type microbeam.

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Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading

Cited by 112 publications

References 21 publications

Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams

Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams

Thermomechanical buckling oftemperature-dependent FGM beams

Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam

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