Quantification of various reduced order modelling computational methods to study deflection of size-dependent plates

Кrysko, V.А.; Awrejcewicz, Jan; Kalutsky, L. A.

doi:10.1016/j.camwa.2023.01.004

Cited by 7 publications

(1 citation statement)

References 46 publications

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“…They concluded that surface effects decrease the deflections. Krysko et al [30] investigated the static analysis of nanoplates exposed to local areas and distributed loads using the modified couple stress theory. They observed that for various boundary conditions and types of loads, the stress-strain state reduces stress and deflection by enhancing the size-dependent parameter.…”

Section: Introductionmentioning

confidence: 99%

The Nonlinear Bending of Sector Nanoplate via Higher-Order Shear Deformation Theory and Nonlocal Strain Gradient Theory

Sadeghian,

Jamil,

Palevicius

et al. 2024

Mathematics

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In this context, the nonlinear bending investigation of a sector nanoplate on the elastic foundation is carried out with the aid of the nonlocal strain gradient theory. The governing relations of the graphene plate are derived based on the higher-order shear deformation theory (HSDT) and considering von Karman nonlinear strains. Contrary to the first shear deformation theory (FSDT), HSDT offers an acceptable distribution for shear stress along the thickness and removes the defects of FSDT by presenting acceptable precision without a shear correction parameter. Since the governing equations are two-dimensional and partial differential, the extended Kantorovich method (EKM) and differential quadrature (DQM) have been used to solve the equations. Furthermore, the numeric outcomes were compared with a reference, which shows good harmony between them. Eventually, the effects of small-scale parameters, load, boundary conditions, geometric dimensions, and elastic foundations are studied on maximum nondimensional deflection. It can be concluded that small-scale parameters influence the deflection of the sector nanoplate significantly.

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Section: Introductionmentioning

confidence: 99%