In this work, a finite element formulation for size dependent frame system is presented. Size dependency discussed via the modified couple stress theory. The nodal displacement and rotation analyses of with total three elements, including two columns one beam connecting these columns, are considered. classical stiffness matrices derived. Then, solution procedure problem explained. Lastly, numer...

This paper deals with the effect of the intrinsic material length-scale parameter on the stability and natural frequency of a rectangular micro-plate for two different cases; fully clamped and fully simply supported. A variational formulation based on Hamilton’s principle and the modified couple stress theory is used to obtain the nonlinear governing equation of a micro-plate incorporating the ...

The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...

In this paper, a size-dependent formulation for the Bernoulli-Euler beam is developed based on a new model of couple stress theory presented by Hadjesfandiari and Dargush. The constitutive equation obtained in this new model, consists of only one length scale parameter that is capable of capturing the micro-structural size effect in predicting the mechanical behavior of the structure. Having on...

In this study, the vibration behavior of functional graded (FG) circular and annular nanoplate embedded in Visco-Pasternak foundation and coupled with temperature change is studied. It is assumed that a uniform radial magnetic field acts on the top surface of the plate and the magnetic permeability coefficient of the plate along its thickness are assumed to vary according to the volume distribu...

Mechanically induced chemical reactivity is a promising means for designing self-sensing and autonomous materials. Force sensitive chemical groups called mechanophores can be covalently linked into polymers in order to trigger specific chemical reactions upon mechanical loading. A model framework is developed to describe the response of these mechanophores to mechanical loading within an elasto...

In this paper, the free vibration behaviors and flexural sensitivity of atomic force microscope cantilevers with small-scale effects are investigated. To study the small-scale effects on natural frequencies and flexural sensitivity, the consistent couple stress theory is applied. In this theory, the couple stress is assumed skew-symmetric. Unlike the classical beam theory, the new model contain...

In this paper, the Elzaki transform method is used for solving two-dimensional (2D) elasticity problems in plane polar coordinates. Airy stress function was used to express the stress compatibility equation as a biharmonic equation. Elzaki transform was applied with respect to the radial coordinate to a modified form of the stress compatibility equation, and the biharmonic equation simplified t...