A size-dependent four variable refined plate model for functionally graded microplates based on modified couple stress theory

He, Liwen; Lou, Jia; Zhang, Enyang; Wang, Yuanchao; Bai, Yang

doi:10.1016/j.compstruct.2015.04.033

Cited by 75 publications

(31 citation statements)

References 35 publications

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“…In this example, the equivalent axial load caused by the thermal stress is calculated with/without the transverse thermal stress Further verification is carried out for mechanical and thermal buckling behaviours of FG plates in Tables 7 and 8. As can be seen in Table 7, the present results of mechanical buckling agree well with those obtained from refined plate theories (RPT) [26,28] and quasi-3D theory [28]. It is also shown that the inclusion of normal stretching effect leads to the higher critical buckling loads for macroplates but less significant to microplates.…”

Section: B Vibration and Buckling Analysissupporting

confidence: 79%

“…Lou et al [27] then developed this model for a unified framework including the von Karman's geometric nonlinearity. It should be noted that above studies [26][27][28][29][30], the normal strain or normal deformation, which becomes significant for thick plates, is not included. In order to take into account both shear and normal deformation effects, Nguyen et al [28] presented four-variable quasi-3D model to analyse the bending, vibration and buckling behaviours of FG microplates using the isogeometric solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Thai and Vo [25] developed a MCST sinusoidal theory for FG microplates and derived analytical solutions for deflections and natural frequencies of simply supported microplates. He et al [26] presented a MCST four-variable refined plate model using analytical solution for the FG microplates. Lou et al [27] then developed this model for a unified framework including the von Karman's geometric nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

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Size-dependent behaviour of functionally graded sandwich microplates under mechanical and thermal loads

Trinh

Thai

et al. 2017

Composites Part B: Engineering

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This paper presents the static bending, free vibration and buckling behaviours of functionally graded sandwich microplates under mechanical and thermal loads. Governing equations of both higher-order shear deformation and quasi-3D theories are derived based on the variational principle and modified couple stress theory. Apart from mechanical load, the temperature profiles considered are either uniform or linear distribution through the thickness, which results in changes of material properties and stress resultants. Numerical results are obtained using Navier solutions. The difference between quasi-3D and 2D models in dealing with mechanical and thermal load is discussed. Temperature-dependent and temperature-independent material properties are examined. The effects of geometry and power-law index together with mechanical loads and various temperature distributions on the size-dependent behaviours of functionally graded sandwich plates are also investigated.

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Section: B Vibration and Buckling Analysissupporting

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Size-dependent behaviour of functionally graded sandwich microplates under mechanical and thermal loads

Trinh

Thai

et al. 2017

Composites Part B: Engineering

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“…Mohammadimehr and Mohandes [34] investigated the e ect of modi ed couple stress theory on buckling and vibration analysis of functionally graded double-layer piezoelectric plates. He et al [35] presented a sizedependent four-variable re ned plate model for functionally graded micro-plates based on modi ed couple stress theory. Shenas and Malekzadeh [36] investigated free vibration of functionally graded quadrilateral micro plates in thermal environment.…”

Section: Introductionmentioning

confidence: 99%

An explicit solution for the size-dependent large amplitude transverse vibration of thin functionally graded micro-plates

Setoodeh

Rezaei

2017

Scientia Iranica

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Abstract. In this article, an analytical solution to the moderately large amplitude transverse vibration of thin Functionally Graded Micro-Plates (FGMPs) is presented based on a practical approach. The size-dependent nonlinear governing equation is obtained in conjunction with the Kirchho 's plate and modi ed couple stress theories. The material properties of Functionally Graded (FG) micro-plates vary according to the Reddy's model. The employed non-classical theory contains one material length-scale parameter to capture the size e ects. The highly nonlinear governing equation is solved by means of homotopy analysis method so as to obtain accurate analytic approximations. Both of simply supported and clamped micro-plates with immovable edges are considered. The comparison made between the present results and those of earlier studies con rms the reliability and e ectiveness of the present formulation for the design purpose. Furthermore, the e ects of di erent parameters, such as material gradient index, length-scale parameter, and aspect ratio, on the nonlinear frequency ratio are investigated.

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“…Sharma and Sharma [30] analyzed the transverse linear dynamics of a generalized thermoelastic circular plate subject to different temperature. He et al [31] developed a size-dependent fourvariable functionally graded microplates employing the modified couple stress theory and Hamilton's principle; they obtained the closed form solutions for linear bending, buckling, and free dynamics of a simply supported microplate. Wang et al [32] derived a size-dependent microplate model by means of the Kirchhoff plate theory based on a strain gradient elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

Internal Energy Transfer in Dynamical Behavior of Slightly Curved Shear Deformable Microplates

Ghayesh

Farokhi

Alici

2015

Journal of Computational and Nonlinear Dynamics

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This paper investigates the internal energy transfer and modal interactions in the dynamical behavior of slightly curved microplates. Employing the third-order shear deformation theory, the microplate model is developed taking into account geometric nonlinearities as well as the modified couple stress theory; the initial curvature is modeled by an initial imperfection in the out-of-plane direction. The in-plane displacements and inertia are retained, and the coupled out-of-plane, rotational, and in-plane motion characteristics are analyzed. Specifically, continuous models are developed for kinetic and potential energies as well as damping and external works; these are balanced and reduced via Lagrange's equations along with an assumed-mode technique. The reduced-order model is then solved numerically by means of a continuation technique; stability analysis is performed by means of the Floquet theory. The possibility of the occurrence of modal interactions and internal energy transfers is verified via a linear analysis on different natural frequencies of the system. The nonlinear resonant response of the system is obtained for the cases with internal energy transfer, and energy transfer mechanisms are analyzed; as we shall see, the presence of an initial curvature affects the system dynamics substantially. The importance of taking into account small-size effects is also shown by discovering this fact that both the linear and nonlinear internal energy transfer mechanisms are shifted substantially if this effect is ignored. This paper investigates the internal energy transfer and modal interactions in the dynamical behavior of slightly curved microplates. Employing the third-order shear deformation theory, the microplate model is developed taking into account geometric nonlinearities as well as the modified couple stress theory; the initial curvature is modeled by an initial imperfection in the out-of-plane direction. The in-plane displacements and inertia are retained, and the coupled out-of-plane, rotational, and in-plane motion characteristics are analyzed. Specifically, continuous models are developed for kinetic and potential energies as well as damping and external works; these are balanced and reduced via Lagrange's equations along with an assumed-mode technique. The reduced-order model is then solved numerically by means of a continuation technique; stability analysis is performed by means of the Floquet theory. The possibility of the occurrence of modal interactions and internal energy transfers is verified via a linear analysis on different natural frequencies of the system. The nonlinear resonant response of the system is obtained for the cases with internal energy transfer, and energy transfer mechanisms are analyzed; as we shall see, the presence of an initial curvature affects the system dynamics substantially. The importance of taking into account small-size effects is also shown by discovering this fact that both the linear and nonlinear internal energy transfer mechanisms are shifted subst...

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A size-dependent four variable refined plate model for functionally graded microplates based on modified couple stress theory

Cited by 75 publications

References 35 publications

Size-dependent behaviour of functionally graded sandwich microplates under mechanical and thermal loads

Size-dependent behaviour of functionally graded sandwich microplates under mechanical and thermal loads

An explicit solution for the size-dependent large amplitude transverse vibration of thin functionally graded micro-plates

Internal Energy Transfer in Dynamical Behavior of Slightly Curved Shear Deformable Microplates

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