Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams

Abstract

The present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.

Wave propagation in magneto-electro-thermo-elastic nanobeams based on nonlocal theory

“…From the one-dimensional nonlocal constitutive relations in Eqs. (7)- (12), it can be obtained as: ,…”

“…The classical beam theory and the Eringen nonlocal elasticity theory are adopted in this paper. Ebrahimi and Barati [12] investigated the thermal buckling behavior of the METE-FG beams subjected several thermal temperature rise and heat conduction by nonlocal and higher-order beam theory. Ma et al [13] analyzed the dispersion characteristics of the MEE nanobeams, and the Euler beam theory and Timoshenko beam theory are conducted.…”

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

“…Non-probabilistic uncertainty modelling for vibration and buckling of the FG nanobeams in nonisothermal conditions is considered in [21]. In the statical analysis, buckling of nonlocal functionally graded beams under thermal loading is frequently addressed, starting from the early contribution in [22] till more recent contributions [23][24][25][26][27]. Mainly nonlocal influence on the mechanical part of the problem is investigated, but buckling caused by the size effect on heat conduction is also analysed [28].…”

Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory

“…Narendar et al [23] investigated wave propagation of MEE-FG nonlocal rods. Also, Ebrahimi and Barati [24][25][26][27] examined free vibration and stability of METE-FG nanobeams based on third-order beam model. According to the above discussion, to the authors' best knowledge, up to now, no study has been carried out on the continuum formulation of buckling behavior of METE-FG nanoplates under external electric and magnetic potentials as well as various thermal environments.…”