A microstructure-dependent orthotropic plate model based on a modified couple stress theory

Abstract

In this paper, a modified couple stress model containing only one material length scale parameter is developed for the static analysis of orthotropic micro-plates with arbitrary shape. The proposed model is capable of handling plates with complex geometries and boundary conditions. From a variational procedure, the governing equilibrium equation of the micro-plate and most of the 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 analogue equation method. Several plates of various shapes, aspect and Poisson's ratios are analysed 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 orthotropic plate model.

A new microstructure-dependent Saint–Venant torsion model based on a modified couple stress theory

“…However, in order to avoid rather complicated computations of singular integrals, the problem is solved using the AEM (Tsiatas and Yiotis, 2010) …”

“…So far it has been developed for the static bending (Park and Gao, 2006) and free vibration (Kong et al, 2008) problems of a Bernoulli-Euler beam, for the static bending and free vibration problems of a Timoshenko beam (Ma et al, 2008) and for the solution of a simple shear problem (Park and Gao, 2008) after the derivation of the boundary conditions and the governing differential equation of the theory in terms of the displacement. Moreover, the static bending problem of Kirchhoff isotropic plates was studied by Tsiatas (2009) and of orthotropic plates by Tsiatas and Yiotis (2010).…”

Vibrations and buckling of orthotropic small‐scale plates with complex shape based on modified couple stress theory

“…[39] analyzed the vibrations of rectangular and circular microplates with various boundary conditions. Tsiatas and Yiotis [40] expanded the using of the modified couple stress theory to an orthotropic plate analysis. Non‐classical Mindlin plate model was developed within the modified couple stress theory and was presented in the work of Ma et al.…”

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

“…Yin et al [16], Simsek et al [17], Jomehzadeh et al [18] employed the modified couple stress theory to vibrations analysis of rectangular and circular microplates with various boundary conditions. Moreover, Tsiatas and Yiotis [19] applied the modified couple stress theory to an orthotropic plate analysis. Ziaee [20] explored the linear vibrations of a rectangular plate with an internal square hole in a thermal environment using the Ritz method.…”