Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams
TL;DR: In this paper, the buckling behavior of nonlocal magneto-electro-elastic functionally graded (MEE-FG) beams is investigated based on a higher-order beam model.
Abstract: In this article, buckling behavior of nonlocal magneto-electro-elastic functionally graded (MEE-FG) beams is investigated based on a higher-order beam model. Material properties of smart nanobeam are supposed to change continuously throughout the thickness based on the power-law model. Eringen's nonlocal elasticity theory is adopted to capture the small size effects. Nonlocal governing equations of MEE-FG nanobeam are obtained employing Hamilton's principle and they are solved using the Navier solution. Numerical results are presented to indicate the effects of magnetic potential, electric voltage, nonlocal parameter and material composition on buckling behavior of MEE-FG nanobeams. Therefore, the present study makes the first attempt in analyzing the buckling responses of higher-order shear deformable (HOSD) MEE-FG nanobeams.
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TL;DR: In this paper, the damping vibration characteristics of hygro-thermally affected functionally graded (FG) viscoelastic nanobeams embedded in a nonlocal strain gradient elasticity theory are investigated.
194 citations
TL;DR: In this article, the buckling characteristics of a curved functionally graded (FG) nanobeam based on nonlocal strain gradient elasticity theory accounting the stress for not only the nonlocal stress field but also the strain gradients stress field were investigated.
154 citations
TL;DR: In this article, the authors examined the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded (FG) nanobeam in thermal environment.
Abstract: This article examines the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded (FG) nanobeam in thermal environment. The theory contains two scale parameters corresponding to both nonlocal and strain gradient effects. A quasi-3D sinusoidal beam theory considering shear and normal deformations is employed to present the formulation. Mori–Tanaka micromechanical model is used to describe functionally graded material properties. Hamilton’s principle is employed to obtain the governing equations of nanobeam accounting for thickness stretching effect. These equations are solved analytically to find the wave frequencies and phase velocities of the FG nanobeam. It is indicated that wave dispersion behavior of FG nanobeams is significantly affected by temperature rise, nonlocality, length scale parameter and material composition.
122 citations
Cites background from "Magnetic field effects on buckling ..."
...Also, Ebrahimi and Barati [27–30] presented vibration and buckling analysis of smart piezoelectrically actuated FG nanobeams subjected to various physical fields....
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TL;DR: In this article, a nonlocal strain gradient theory was used to capture size effects in wave propagation analysis of compositionally graded smart nanoplates, where a power law function is used to describe the material distribution across the thickness of functionally graded (FG) nanoplate.
101 citations
TL;DR: In this paper, the free vibration of three-directional functionally graded material (TDFGM) Euler-Bernoulli nano-beam, with small scale effects, is investigated.
94 citations
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TL;DR: In this article, the integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels.
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TL;DR: In this article, the dispersion relations for one dimensional plane waves were obtained by fitting the nonlocal material moduli to exactly the acoustical branch of elastic waves within one Brillouin zone in periodic one dimensional lattices.
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TL;DR: In this paper, a variational formulation is employed to derive a micromechanics-based, explicit nonlocal constitutive equation relating the ensemble averages of stress and strain for a class of random linear elastic composite materials.
Abstract: A variational formulation is employed to derive a micromechanics-based, explicit nonlocal constitutive equation relating the ensemble averages of stress and strain for a class of random linear elastic composite materials. For two-phase composites with any isotropic and statistically uniform distribution of phases (which themselves may have arbitrary shape and anisotropy), we show that the leading-order correction to a macroscopically homogeneous constitutive equation involves a term proportional to the second gradient of the ensemble average of strain. This nonlocal constitutive equation is derived in explicit closed form for isotropic material in the one case in which there exists a well-founded physical and mathematical basis for describing the material's statistics: a matrix reinforced (or weakened) by a random dispersion of nonoverlapping identical spheres. By assessing, when the applied loading is spatially-varying, the magnitude of the nonlocal term in this constitutive equation compared to the portion of the equation that relates ensemble average stresses and strains through a constant “overall” modulus tensor, we derive quantitative estimates for the minimum representative volume element (RVE) size, defined here as that over which the usual macroscopically homogeneous “effective modulus” constitutive models for composites can be expected to apply. Remarkably, for a maximum error of 5% of the constant “overall” modulus term, we show that the minimum RVE size is at most twice the reinforcement diameter for any reinforcement concentration level, for several sets of matrix and reinforcement moduli characterizing large classes of important structural materials. Such estimates seem essential for determining the minimum structural component size that can be treated by macroscopically homogeneous composite material constitutive representations, and also for the development of a fundamentally-based macroscopic fracture mechanics theory for composites. Finally, we relate our nonlocal constitutive equation explicitly to the ensemble average strain energy, and show how it is consistent with the stationary energy principle.
857 citations