Effect of magnetic-thermal field on nonlinear wave propagation of circular nanoplates

Allahyari, Ehsan; Asgari, Masoud

doi:10.1080/09205071.2019.1677271

Cited by 5 publications

(6 citation statements)

References 34 publications

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“…4. [See Eq. (35).] • The mentioned concentrated force acting at the center of the plate is zero for the local case, * = 0.…”

Section: Discussionmentioning

confidence: 99%

“…(5)(6)(7)(8), and the boundary conditions (9) of a SSP subjected to a uniformly distributed load q * and the concentrated force F * , defined in Eq. (35), acting at the center of the circular nanoplate.…”

Section: Analysis For the Simply Supported Circular Nanoplatementioning

confidence: 99%

“…An unknown (nondimensional) redundant axisymmetric support moment X * , acting at r * = 1 , is considered to be superposed to the nonlocal solution obtained for a SSP subjected to a uniformly distributed load q * and the concentrated force F * , defined in Eq. (35). Accordingly, the nonlocal expression for the deflection of CP can be written as…”

Section: Analysis For the Clamped Nanoplatementioning

confidence: 99%

“…It has been observed, interestingly, in this study that the size effect and the specific nonlocal concentrated force, defined in Eq. (35), seem to compensate each other for M * r in SSP case and w * in CP case, making these variables to be equal to their corresponding local counterparts for the uniformly distributed load only. Somewhat similarly, considering the uniformly distributed load only, there was no nonlocal effect on M * r in SSP case and w * in CP case in the study presented by Duan and Wang [47], as well.…”

Section: Comparative Analysismentioning

confidence: 99%

“…(1), of the Eringen's nonlocal model to the bending of nanobeams, Eq. (1) was applied to a host of problems of nanomechanics including those pertaining to the bending, stability and vibration of the structural elements (rods, plates and shells) , among which the circular nanoplates were taken a special interest by researchers and engineers [32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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Exact nonlocal solutions of circular nanoplates subjected to uniformly distributed loads and nonlocal concentrated forces

Yükseler

2019

J Braz. Soc. Mech. Sci. Eng.

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The nonlocal solutions of the bending problem of the circular elastic nanoplates subjected to uniformly distributed loads by using the Eringen's nonlocal theory are approximate. Seeking for an exact solution of the concerning problem by adding a concentrated force; a specific concentrated force which depends on the nonlocal parameter and, therefore, vanishes in the local case, is obtained. In this context; starting from the local bending solution of the simply supported circular nanoplates under uniformly distributed loads and evolving the solution step by step, exact nonlocal solutions of the bending problem of the simply supported and clamped circular nanoplates subjected to uniformly distributed loads and the concerning nonlocal concentrated forces acting at the centers of the circular nanoplates are obtained with the expectation that the exact nonlocal solution is not very different than the corresponding exact local solution. The closed-form solutions are checked to satisfy exactly the equations of equilibrium, constitutive equations and the boundary conditions of the relevant nonlocal problem. The application of the concerning specific concentrated force, in addition to the uniformly distributed load, is seen to make the radial bending moments for the simply supported circular nanoplate and the deflections for the clamped circular nanoplate free from the effects of the nonlocality.

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“…4. [See Eq. (35).] • The mentioned concentrated force acting at the center of the plate is zero for the local case, * = 0.…”

Section: Discussionmentioning

confidence: 99%