Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory

Karami, Behrouz; Janghorban, Maziar; Tounsi, Abdelouahed

doi:10.1016/j.tws.2018.02.025

Cited by 169 publications

(33 citation statements)

References 51 publications

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“…where the constants d 1 to d 23 are presented in "Appendix C." Solving two Eqs. (18) and (19) simultaneously the displacements along two directions, elliptic cylindrical and hyperbolic cylindrical, is specified. The boundary condition for Eqs.…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…He considered various boundary conditions for the plates and investigated the effects of gradient indexes and directions on the behavior of the plates. Behrouz et al [18], based on a new non-local strain gradient, used variational approach for wave dispersion in doubly curved anisotropic nanoshells. Atrian et al [19] studied the analytical solution of a thick-walled functionally graded hollow cylinder under non-axisymmetric thermo-mechanical loads.…”

Section: Introductionmentioning

confidence: 99%

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Thermo-mechanical behavior of a functionally graded hollow cylinder with an elliptic hole

Fesharaki

Roghani

2019

J Braz. Soc. Mech. Sci. Eng.

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In this paper, the behavior of functionally graded material hollow cylinders with an elliptic hole under thermal and mechanical loads is investigated. The problem is considered as plane strain condition, and to obtain the governing equations and boundary condition for this complex geometry, an elliptic cylindrical coordinate is used. The material properties are considered to vary along the elliptic cylindrical direction with power-law function except for the Poisson's ratio. To solve the two coupled differential equations, differential quadrature method is used. For solving the governing equations, two different boundary conditions are considered for thermal and mechanical loads. The results show that unconventional shape for a hole in the cylinder can affect the results expected such as stresses or displacements, and this information about thermo-mechanical loads can be used for designing the advanced sensors. Also with considering special material index, the stress and displacement along the cylinder can be controlled. The presented results in this paper are verified with those reported in the previous publication.

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Section: Mathematical Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermo-mechanical behavior of a functionally graded hollow cylinder with an elliptic hole

Fesharaki

Roghani

2019

J Braz. Soc. Mech. Sci. Eng.

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“…A further application of the nonlocal elasticity theory can be found in Reference [23] for a parametric study of the axial post-buckling behavior of nanoshells with different nonlocal parameters. Various nonlocal theories have been applied within coupled problems, such as piezoelectric, flexoelectric, or thermo-electro-mechanical shells at different scales both for simple [24][25][26][27][28][29][30][31][32] or more complex [33][34][35][36][37][38][39][40][41][42][43][44][45][46] geometries.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Elasticity Response of Doubly-Curved Nanoshells

Dindarloo

Dimitri

et al. 2020

Symmetry

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In this paper, we focus on the bending behavior of isotropic doubly-curved nanoshells based on a high-order shear deformation theory, whose shape functions are selected as an accurate combination of exponential and trigonometric functions instead of the classical polynomial functions. The small-scale effect of the nanostructure is modeled according to the differential law consequent, but is not equivalent to the strain-driven nonlocal integral theory of elasticity equipped with Helmholtz’s averaging kernel. The governing equations of the problem are obtained from the Hamilton’s principle, whereas the Navier’s series are proposed for a closed form solution of the structural problem involving simply-supported nanostructures. The work provides a unified framework for the bending study of both thin and thick symmetric doubly-curved shallow and deep nanoshells, while investigating spherical and cylindrical panels subjected to a point or a sinusoidal loading condition. The effect of several parameters, such as the nonlocal parameter, as well as the mechanical and geometrical properties, is investigated on the bending deflection of isotropic doubly-curved shallow and deep nanoshells. The numerical results from our investigation could be considered as valid benchmarks in the literature for possible further analyses of doubly-curved applications in nanotechnology.

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“…Mehralian et al [107] calibrated their results for buckling phenomena in carbon nanotubes using MD simulation. The results of wave propagation and vibration problems in graphene sheet were calibrated with experimental date by Karami and his co-workers [108][109][110]. Furthermore, Li et al [111,112] calibrated their size-dependent plate model with experimental data to find suitable length scale parameters for mechanical analysis of nanostructures but most of the researchers just study the variations of length scale parameters without finding the exact value for them [80][81][82][83][84][85][86][87][88][89][90][91][92][93][94].…”

Section: Introductionmentioning

confidence: 99%

On pre-stressed functionally graded anisotropic nanoshell in magnetic field

Karami

Janghorban

Tounsi

2019

J Braz. Soc. Mech. Sci. Eng.

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Elastic bulk wave characteristics of doubly curved nanoshell made of functionally graded (FG) anisotropic material are studied. The effective properties of FG anisotropic material vary along the thickness direction. A higher-order shear deformation shell theory and the Bi-Helmholtz nonlocal strain gradient theory are, respectively, utilized to model the nanoshell as a continuum model and predicting the size-dependent behavior. The Hamiltonian principle is adopted to obtain the governing equations of wave motion. These equations are solved analytically to evaluate the wave characteristics of the nanoshell. Emphasizing the effect of parametric excitation, the influences of small-scale parameters, exponential factor, magnetic field intensity, initial stress, elastic foundation parameters, and wave number are assessed on the wave dispersion response of FG anisotropic nanoshell.

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Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory

Cited by 169 publications

References 51 publications

Thermo-mechanical behavior of a functionally graded hollow cylinder with an elliptic hole

Thermo-mechanical behavior of a functionally graded hollow cylinder with an elliptic hole

Nonlocal Elasticity Response of Doubly-Curved Nanoshells

On pre-stressed functionally graded anisotropic nanoshell in magnetic field

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