The novelty of this study is presentation of an exact solution for prediction of postbuckling behavior of shear deformable micro- and nano-scale beams based on modified couple stress theory and using principle of minimum potential energy. Timoshenko and Reddy-Levinson beam theories are applied to consider the shear deformation effect and Von Karman nonlinear kinematics is used to describe the n...

in classical mechanics, considering hook’s law stress is a linear function of strain. while in strain gradient theory stress is a function of strain and strain differentials. in this paper, novel formulation relating stress and strain and also new boundary conditions are derived based on minimum potential energy principle. in strain gradient theory a length coefficient parameter is defined. thi...

the arya and paris model is a commonly accepted method to translate a particle-size distribution curve into a corresponding soil moisture characteristic curve using scaling parameter (α). the scaling parameter, in the original model of arya and paris (1981), was assumed constant (α=1.38) for all soil texture classes. in recent years, several studies have shown that α is not constant and its qua...

In this paper, the Ritz method has been employed to analyze the free in-plane vibration of heterogeneous (non-uniform) rectangular nanoplates corresponding to Eringen’s nonlocal elasticity theory. The non-uniformity is taken into account using combinations of linear and quadratic forms in the thickness, material density and Young’s modulus. Two-dimensional boundary characteristic orthogonal pol...

A parallel algorithm for detecting dominant points on a digital closed curve is presented. The procedure requires no input parameter and remains reliable even when features of multiple sizes are present on the digital curve. The procedure first determines the region of support for each point based on its local properties, then computes measures of relative significance (e.g., curvature) of each...

In this article, the size effect on the dynamic behavior of a simply supported multi-cracked microbeam is studied based on the Modified Couple Stress Theory (MCST).  At first, based on MCST, the equivalent torsional stiffness spring for every open edge crack at its location is calculated; in this regard, the Stress Intensity Factor (SIF) is al...

In this article, the effect of size-dependent on the buckling and vibration analysis of functionally graded (FG) double-layer boron nitride plate based on classical plate theory (CPT) under electro-thermo-mechanical loadings which is surrounded by elastic foundation is examined. This subject is developed using modified couple stress theory. Using Hamilton's principle, the governing equations of...

deflection analysis of a simply supported microbeam subjected to a concentrated load at the middle is investigated on the basis of a shear deformable beam theory and non-classical theory. effects of shear deformation and small size are taken into consideration by hyperbolic shear deformable beam theory and modified strain gradient theory, respectively. the governing differential equations and c...

In the present study, a vibration analysis of functionally graded rectangular nano-/microplates was considered based on modified nonlinear coupled stress exponential and trigonometric shear deformation plate theories. Modified coupled stress theory is a non-classical continuum mechanics theory. In this theory, a material-length scale parameter is applied to account for the effect of nanostructu...