A new Kirchhoff plate model based on a modified couple stress theory

Abstract

a b s t r a c tIn this paper a new Kirchhoff plate model is developed for the static analysis of isotropic micro-plates with arbitrary shape based on a modified couple stress theory containing only one material length scale parameter which can capture the size effect. The proposed model is capable of handling plates with complex geometries and boundary conditions. From a detailed variational procedure the governing equilibrium equation of the micro-plate and the most general boundary conditions are derived, in terms of the deflection, using the principle of minimum potential energy. The resulting boundary value problem is of the fourth order (instead of existing gradient theories which is of the sixth order) and it is solved using the Method of Fundamental Solutions (MFS) which is a boundary-type meshless method. Several plates of various shapes, aspect and Poisson's ratios are analyzed to illustrate the applicability of the developed micro-plate model and to reveal the differences between the current model and the classical plate model. Moreover, useful conclusions are drawn from the micron-scale response of this new Kirchhoff plate model.

The Influence of Couple Stress Components and Electrostatic Actuation on Free Vibration Characteristics of Thin Micro-Plates

“…It is worth noting that this important conclusion has also been reported numerically by Tsiatas [19] and analytically by Askari and Tahani [20] …”

“…Hence, the main object of the present paper is to investigate the effects of size and electrostatic loading on the free vibration characteristics of electrically actuated thin micro-plates as one of the most important building blocks of MEMS devices. To this end, the size-dependent Kirchhoff thin plate model [19] is employed to develop the equation which governs on the linear free vibration of the system. Using this governing equation, it is proved that the micro-plate linear mode-shapes are totally independent of size and electrostatic loading.…”

“…That is, x , ŷ and ẑ are the coordinates along the width, length and thickness, respectively. According to the MCSTbased size-dependent thin plate model presented by Tsiatas [19], the governing equation of motion takes the form [16] …”

Effect of size dependency on in-plane vibration of circular micro-rings

“…Fakhrabadi et al [29] analyzed the nonlinear vibration of carbon nanotubes based on modi ed couple stress theory. Tsiatas [30] utilized the modi ed couple stress theory to develop the size-dependent formulation of Kirchho plates. The formulations of laminated Reddy and Kirchho micro plates derived based on the modi ed couple stress theory were presented by Chen et al [31,32].…”

Size-Dependent Bending, Buckling and Free Vibration Analyses of Microscale Functionally Graded Mindlin Plates Based on the Strain Gradient Elasticity Theory

“…In this direction, the modified couple stress theory (MCST) was initiated by Yang et al (2002) in which only one length scale parameter is used in the constitutive equations leading to the symmetric couple stress tensor. Relevant works concerning the applicability of MCST in the analysis of microstructures can be found in (Ma et al (2008); Tsiatas (2009); Kahrobaiyan et al (2010); Ke et al (2011);Jomehzadeh et al (2011); Asghari (2012); Thai and Choi (2013)). In addition to these works, based on the modified couple stress and Kirchhoff plate theories, a size-dependent plate model was developed by Yin et al (2010) for the dynamic analysis of microplate.…”