A size-dependent functionally graded sinusoidal plate model based on a modified couple stress theory

Thai, Huu‐Tai; Vo, Thuc P.

doi:10.1016/j.compstruct.2012.09.025

Cited by 98 publications

(22 citation statements)

References 30 publications

(34 reference statements)

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“…Akgöz and Civalek [36] presented a new non-classical sinusoidal plate model on the basis of modified strain gradient theory to investigate bending, buckling and vibration behavior. In addition to the above studies, the modified couple stress theory is also used to study the behavior of microbeams and microplates made of composite materials [37][38][39][40][41][42][43][44][45][46][47][48][49].…”

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confidence: 99%

Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

et al. 2015

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This study deals with forced vibration analysis of a microplate subjected to a moving load. The formulation is developed based on the modified couple stress theory in conjunction with Kirchhoff-Love plate theory. The equations of motion of the problem are derived using Lagrange's equations. In order to obtain the response of the microplate, the trial function for the dynamic deflection is expressed in the polynomial form. The equations of motion are solved by using the implicit time integration Newmark-β method, and then displacements, velocities and accelerations of the microplate at the considered point and time are determined. Five different sets of boundary condition are considered. For this purpose, boundary conditions are satisfied by adding some auxiliary functions to the trial functions. A parametric study is conducted to study the effects of the material length scale parameter, plate aspect ratio, boundary conditions and the moving load velocity on the dynamic response of the microplate. Also, in order to validate the present formulation and solution method, some comparisons with those available in the literature are performed. Good agreement is found. The results show that the dynamic deflections are significantly affected by the scale parameter and the load velocity.

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confidence: 99%

Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

et al. 2015

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“…Despite the significance of FG microstructures, several studies are devoted to explore the mechanical responses of these phenomenal structures [26][27][28][29][30][31][32][33][34][35][36]. In this direction, based upon the MSGT, Ansari et al [37] examined the nonlinear free vibration characteristics of FG Timoshenko microbeams.…”

Section: Introductionmentioning

confidence: 98%

Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin's strain gradient theory

Ansari

Gholami

Shojaei

et al. 2016

Applied Mathematical Modelling

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1 Highlights  Development of a nonlinear first-order shear deformable small-scale beam model  Presenting formulation based on the most general Mindlin's strain gradient theory  Prediction of coupled free vibration of post-buckled micro-and nano-beams with various BCS  Study of the effects of ⁄ , ⁄ , and BCs on the postbuckling path and frequency  Comparing the results predicted by CT, MCST and MSGT Abstract Presented herein is a comprehensive study on the size-dependent coupled longitudinal-transverserotational free vibration behavior of post-buckled functionally graded (FG) micro-and nano-beams based on the most general Mindlin's strain gradient theory. The current model enables us to incorporate size effects via introducing material length scale parameters and is developed in the framework of the firstorder shear deformable beam model and the von Karman geometric nonlinearity. The FG micro-and nano-beams, whose volume fraction is expressed by using a power law function, are assumed to be made of a mixture of metals and ceramics. By using Hamilton's principle, the nonlinear governing equations and associated boundary conditions are derived for FG micro-and nano-beams in the postbuckling domain. Afterwards, the governing equations and boundary conditions are discretized using the generalized differential quadrature (GDQ) method in conjunction with a direct approach without linearization, before solving numerically by Newton's method. The effects of length scale parameter, length-to-thickness ratio, material gradient index and boundary conditions on the postbuckling path and frequency of FG micro-and nano-beams are carefully investigated. Finally, numerical results obtained from both the modified strain gradient theory (MSGT) and modified couple stress theory (MCST) are compared.Mindlin's strain gradient elasticity; Size-dependent first-order shear deformable beam model.

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“…Static bending analysis: [25]. It is also seen that quasi-3D models provide higher deflections for small-scale plates but lower values for thicker plates compared to 2D models.…”

Section: Verificationmentioning

confidence: 99%

“…These models were applied to investigate bending and free vibration behaviours of FG microplates by Thai and Kim [23] using analytical solutions and annular/circular microplates by Eshraghi [24] using the differential quadrature (DQ) method. 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.…”

Section: Introductionmentioning

confidence: 99%

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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A size-dependent functionally graded sinusoidal plate model based on a modified couple stress theory

Cited by 98 publications

References 30 publications

Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin's strain gradient theory

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

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