This paper investigates the buckling and free vibration analysis of functionally graded carbon nanotube-reinforced composite thick rectangular nanoplates resting on a Kerr foundation under different boundary conditions. Quasi-three-dimensional hyperbolic shear deformation theory is employed to study the effects of transverse shear deformation and thickness stretching. To capture the small-size effects of nanoscale dimensions, the nonlocal strain gradient theory is used, which includes nonlocal parameters and length scale of the material. In this study, rectangular nanocomposite plates are reinforced by carbon nanotubes which are assumed to be graded through the thickness direction with four types of distributions, namely, uniformly, FG-O, FG-V, and FG-X. The governing equations and boundary conditions are extracted within Hamilton’s principle. They are discretized and numerically solved by utilizing a generalized differential quadrature method. The critical buckling loads and natural frequencies are determined by solving the eigenvalue problem. The accuracy of present results is validated with those available in the literature. Also, the effect of various factors, such as aspect ratio, length-to-thickness ratio, in-plane loading factor, length scale parameter, nonlocal parameter, volume fraction and dispersion profile of carbon nanotubes, elastic foundation coefficients, and different boundary conditions, on the buckling behavior and free vibration of nanoplates is investigated.

boundary conditions, lateral and shear stiffness coefficients of elastic foundation are examined on critical buckling.

This article examines the application of simplified Mindlin’s strain gradient theory to free vibration analysis of functionally graded carbon nanotube–reinforced composite (FG-CNTRC) thick rectangular nanoplates resting on Kerr elastic foundation in thermal environment. The theory contains only one length scale parameter corresponding to strain gradient effects. Also, a quasi-3D hyperbolic theory considering transverse shear deformation and thickness stretching effects is employed to present the formulation. In this study, properties of the carbon nanotubes (CNTs) and the polymeric matrix are assumed to be temperature dependent. Distribution of CNTs across the thickness of the nanoplate is considered to be uniform (UD) or functionally graded (FG-X, FG-V, and FG-O). According to Hamilton’s principle and the generalized differential quadrature method, the governing equations and associated boundary conditions are obtained and discretized, respectively. The natural frequencies of FG-CNTRC nanoplates are determined by solving eigenvalue problem. The numerical results of the present formulation are compared with those available in the literature to explain the accuracy of the suggested theories. Then, parametric studies are presented to examine the effects of elastic foundation coefficients, size parameter, temperature change, volume fraction and dispersion profile of CNTs, aspect ratio, length-to-thickness ratio, and different boundary conditions on vibration behavior of FG-CNTRC nanoplates. The results confirmed that size parameter and changes in temperature play an important role in determining natural frequencies. In addition, the shear layer parameter of Kerr foundation has more influence with respect to the coefficients of the upper and lower layers.

This article covers the state-of-the-art light stabilizer for rotational molding and the influence of synergistic effects between light and thermal stabilizers, which improve physical and mechanical properties. Different formulations of polyethylene (PE) with light stabilizer, thermal stabilizer, and acid scavenger have been produced in twinscrew extruder. To study the light stability, sheets that produced by injection-molding machine have been put in weather-ometer instrument for 1000 h. After and before that, physical and mechanical properties have been evaluated.