Analysis Of Nanoplates Research Articles

New higher-order shear deformation theory for bending analysis of the two-dimensionally functionally graded nanoplates

In this study, we focus on the bending analysis of the 2 D FG nanoplate based on a new high-order shear deformation theory (HSDT). This kind of HSDT is one of the most accurate HSDT because the shape functions are selected as an accurate combination of exponential, trigonometric and polynomial functions. The mechanical properties of the nanoplate vary along the length and thickness, based on arbitrary functions. The small scale effect of the nanostructure is modeled according to the nonlocal theory of elasticity. The governing equations of the problem are obtained from Hamilton’s principle, whereas the Galerkin method is proposed for a closed-form solution of the structural problem for simply-supported nanostructures. The work provides a unified framework for the mechanical analysis of both thin and thick plates. The effect of several parameters, such as the nonlocal parameter, as well as the mechanical and geometrical properties and FG indexes, are investigated on the bending deflection of the 2 D FG nanoplates. The numerical results from our investigation could be considered as valid benchmarks in the literature for possible further analyses of nanoplates.

Nonlocal microstructure-dependent dynamic stability of refined porous FG nanoplates in hygro-thermal environments

Based on the generalized nonlocal strain gradient theory (NSGT), dynamic modeling and analysis of nanoporous inhomogeneous nanoplates is presented. Therefore, it is possible to capture both stiffness-softening and stiffness-hardening effects for a more accurate dynamic analysis of nanoplates. The nanoplate is in hygro-thermal environments and is subjected to an in-plane harmonic load. Porosities are incorporated to the model based on a modified rule of mixture. Modeling of the porous nanoplate is conducted according to a refined four-variable plate theory with fewer field variables than in the first-order plate theory. The governing equations and related classical and nonclassical boundary conditions are derived based on Hamilton’s principle. These equations are solved for hinged nanoplates via Galerkin’s method. It is shown that porosities, moisture rise, temperature rise, nonlocal parameter, strain gradient parameter, material gradation, elastic foundation and uniform dynamic load have a remarkable influence on the dynamic behavior of nanoscale plates.

Thermal buckling analysis of nanoplates based on nonlocal elasticity theory with four-unknown shear deformation theory resting on Winkler–Pasternak elastic foundation

ABSTRACTThe thermal buckling analysis of nanoplates is based on nonlocal elasticity theory with four-unknown shear deformation theory resting on Winkler–Pasternak elastic foundation. The nanoplate is assumed to be under three types of thermal loadings, namely uniform temperature rise, linear temperature rise, and nonlinear temperature rise through the thickness. The theory involves four unknown variables with small-scale effects, as against five in the case of other higher-order theories and first-order shear deformation theory. Closed-form solution for theory was also presented. Results are presented to discuss the influences of the nonlocal parameter, aspect ratio, side-to-thickness ratio, and elastic foundation parameters on the thermal buckling characteristics of analytical rectangular nanoplates.

Analysis of nano-plates by atomistic-refined models accounting for surface free energy effect

This work presents several higher-order atomistic-refined models for the static and free vibration analysis of nano-plates. Stemming from a two-dimensional approach and thanks to a compact notation for the a priori kinematic field approximation over the plate through-the-thickness direction, a general model derivation is used where the approximation order is a free parameter of the formulation. Several higher-order plate theories can be obtained straightforwardly. Classical plate models, such as Kirchhoff’s and Reissner’s, are obtained as particular cases. The assumed constitutive equations for orthotropic materials are those derived by Dingreville et al. (J Mech Phys Solids 53:1827–1854, 2005), which account for the surface free energy effect as well as the third-order elastic constants. The resulting stiffness coefficients depend upon the thickness. The governing equations and boundary conditions are variationally obtained through the principle of virtual displacements. A Navier-type, strong form solution is adopted. Simply supported plates are, therefore, investigated. Static and free vibration analyses are carried out in order to investigate the effect of the thickness side as well as the crystallographic plane orientation on the mechanical response. Plates with different values of the side-to-thickness ratio are considered. Results are validated in terms of accuracy and computational costs toward three-dimensional FEM solutions. Numerical investigations show the advantages of refined plate models over the classical ones demonstrating that accurate results can be obtained with reduced computational costs.