Size effect on the static, dynamic and buckling analysis of orthotropic Kirchhoff-type skew micro-plates based on a modified couple stress theory: comparison with the nonlocal elasticity theory

Tsiatas, George; Yiotis, Aristophanes J.

doi:10.1007/s00707-014-1249-3

Cited by 59 publications

(18 citation statements)

References 38 publications

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“…Akgöz and Civalek [33] studied the buckling response of size-dependent functionally graded (FG) microbeams for different boundary conditions. Tsiatas and Yiotis [34] studied the static, dynamic and buckling behavior of an orthotropic skew microplate based on the modified couple stress theory using the analog equation method (AEM). Kahrobaiyan et al [35] established a beam element that recovers the formulations of strain gradient, modified couple stress and classical Timoshenko and Euler-Bernoulli beam elements by using strain gradient theory.…”

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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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“…The solution by the Ritz method proposed in the paper is denoted as RS. The orthotropic square plate with a free edge and others clamped edges are studied for the following mechanical and geometrical data [21]:…”

Section: Resultsmentioning

confidence: 99%

“…Ziaee [20] explored the linear vibrations of a rectangular plate with an internal square hole in a thermal environment using the Ritz method. Investigation of bending, buckling and vibrations of an orthotropic skew plate was performed by Tsiatas and Yiotis [21].…”

Section: Introductionmentioning

confidence: 99%

Ritz Method in Vibration Analysis for Embedded Single-Layered Graphene Sheets Subjected to In-Plane Magnetic Field

Mazur

Awrejcewicz

2020

Symmetry

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Vibrations of single-layered graphene sheets subjected to a longitudinal magnetic field are considered. The Winkler-type and Pasternak-type foundation models are employed to reproduce the surrounding elastic medium. The governing equation is based on the modified couple stress theory and Kirchhoff–Love hypotheses. The effect of the magnetic field is taken into account due to the Lorentz force deriving from Maxwell’s equations. The developed approach is based on applying the Ritz method. The proposed method is tested by a comparison with results from the existing literature. The numerical calculations are performed for different boundary conditions, including the mixed ones. The influence of the material length scale parameter, the elastic foundation parameters, the magnetic parameter and the boundary conditions on vibration frequencies is studied. It is observed that an increase of the magnetic parameter, as well as the elastic foundation parameters, brings results closer to the classical plate theory results. Furthermore, the current study can be applied to the design of microplates and nanoplates and their optimal usage.

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“…It was supposed that the plate is subjected to linearly distributed in-plane loads on two opposite edges. Tsiatas and Yiotis [31] studied the size effect on the orthotropic Kirchhoff type of skew micro-plates according to the modified couple stress theory. They considered one length scale parameter to capture the size effect in the 2D couple stress theory.…”

Section: Introductionmentioning

confidence: 99%

An analytical solution for buckling analysis of size-dependent rectangular micro-plates according to the modified strain gradient and couple stress theories

Mohammadi

Mahani

2015

Acta Mech

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In this study, a size-dependent Kirchhoff plate model is developed for determining the critical buckling loads of rectangular micro-plates. Modified strain gradient theory with three length scale parameters is used. It should be noted that this theory is reduced to modified couple stress theory by setting two length scale parameters to zero. Using the variational approach and the principle of minimum total potential energy, the nonlinear form of the governing equations and all possible boundary conditions are determined. It is assumed that the micro-plate is simply supported on two opposite edges. The stability equations are solved analytically, and the critical buckling loads are obtained based on the modified strain gradient and modified couple stress theories. Also, the effects of length scale parameters, dimensions and loading states on the buckling loads are investigated in detail.

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Size effect on the static, dynamic and buckling analysis of orthotropic Kirchhoff-type skew micro-plates based on a modified couple stress theory: comparison with the nonlocal elasticity theory

Cited by 59 publications

References 38 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

Ritz Method in Vibration Analysis for Embedded Single-Layered Graphene Sheets Subjected to In-Plane Magnetic Field

An analytical solution for buckling analysis of size-dependent rectangular micro-plates according to the modified strain gradient and couple stress theories

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