• Steel and Composite Structures
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• v.50 no.5
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• pp.563-581
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• 2024

This paper presents a novel finite element model for the free vibration analysis of variable-thickness functionally graded porous (FGP) microplates resting on Pasternak's medium in the hygro-thermal environment. The governing equations are established according to refined higher-order shear deformation plate theory (RPT) in construction with the modified couple stress theory. For the first time, three-node triangular elements with twelve degrees of freedom for each node are developed based on Hermitian interpolation functions to describe the in-plane displacements and transverse displacements of microplates. Two laws of variable thickness of FGP microplates, including the linear law and the nonlinear law in the x-direction are investigated. Effects of thermal and moisture changes on microplates are assumed to vary continuously from the bottom surface to the top surface and only cause tension loads in the plane, which does not change the material's mechanical properties. The numerical results of this work are compared with those of published data to verify the accuracy and reliability of the proposed method. In addition, the parameter study is conducted to explore the effects of geometrical and material properties such as the changing law of the thickness, length-scale parameter, and the parameters of the porosity, temperature, and humidity on the free vibration response of variable thickness FGP microplates. These results can be applied to design of microelectromechanical structures in practice.

• Steel and Composite Structures
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• v.50 no.4
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• pp.403-418
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• 2024

In this paper, vibration and energy absorption characteristics of a nanostructure which is composed of two embedded porous annular/circular nanoplates coupled by a viscoelastic substrate are investigated. The modified couple stress theory (MCST) and the Gurtin-Murdoch theory are applied to take into account the size and the surface effects, respectively. Furthermore, the structural damping effect is probed by the Kelvin-Voigt model and the mathematical model of the problem is developed by a new hyperbolic higher order shear deformation theory. The differential quadrature method (DQM) is employed to obtain the out-of-phase and in-phase frequencies of the structure in order to predict the dynamic response of it. The acquired results reveal that the vibration and energy absorption of the system depends on some factors such as porosity, surface stress effects, material length scale parameter, damping and spring constants of the viscoelastic foundation as well as geometrical parameters of annular/circular nanoplates. A bird's-eye view of the findings in the research paper offers a comprehensive understanding of the vibrational behavior and energy absorption capabilities of annular/circular porous nanoplates. The multidisciplinary approach and the inclusion of porosity make this study valuable for the development of innovative materials and applications in the field of nanoscience and engineering.

• Advances in nano research
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• v.9 no.3
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• pp.193-210
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• 2020

In this research, beside presenting real images of produced Functionally Graded Carbon Nanotube-Reinforced Composites (FG-CNTRCs) and a brief review of the synthesis method of FG-CNTRCs, static and buckling analysis of FG-CNTRC with piezoelectric layers are investigated. It is assumed that the material properties of FG-CNTRC are varied through the thickness direction using four different distributions of Carbon Nanotubes (CNTs). To capture the size effects, nonlocal elasticity theory proposed by A.C. Eringen is also adopted in our model. One of the topics in our paper is using a higher order theory with eight different displacement fields and comparing their results with each other. To solve the governing equations, an analytical method is used to find the deflections and critical buckling loads of FG-CNTRCs. To show the accuracy of present methodology, our results are compared with the results of simply supported rectangular nano plates available in the literature. In this research, the effects of aspect ratio, piezoelectric layer and nonlocal parameter are also studied. It is hoped that this work leads to more accurate models on FG-CNTRC.

• Advances in nano research
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• v.12 no.2
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• pp.117-137
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• 2022

Effect of thickness stretching on free vibration, bending and buckling behavior of carbon nanotubes reinforced composite (CNTRC) laminated nanoplates rested on new variable elastic foundation is investigated in this paper using a developed four-unknown quasi-3D higher-order shear deformation theory (HSDT). The key feature of this theoretical formulation is that, in addition to considering the thickness stretching effect, the number of unknowns of the displacement field is reduced to four, and which is more than five in the other models. Two new forms of CNTs reinforcement distribution are proposed and analyzed based on cosine functions. By considering the higher-order nonlocal strain gradient theory, microstructure and length scale influences are included. Variational method is developed to derive the governing equation and Galerkin method is employed to derive an analytical solution of governing equilibrium equations. Two-dimensional variable Winkler elastic foundation is suggested in this study for the first time. A parametric study is executed to determine the impact of the reinforcement patterns, nonlocal parameter, length scale parameter, side-t-thickness ratio and aspect ratio, elastic foundation and various boundary conditions on bending, buckling and free vibration responses of the CNTRC plate.

• Structural Engineering and Mechanics
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• v.86 no.6
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• pp.731-738
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• 2023

This article presents an analytical approach to explore the bending behaviour of of two-dimensional (2D) functionally graded (FG) nanobeams based on a two-variable higher-order shear deformation theory and nonlocal strain gradient theory. The kinematic relations are proposed according to novel trigonometric functions. The material gradation and material properties are varied along the longitudinal and the transversal directions. The equilibrium equations are obtained by using the virtual work principle and solved by applying Navier's technique. A comparative evaluation of results against predictions from literature demonstrates the accuracy of the proposed analytical model. Moreover, a detailed parametric analysis checks for the sensitivity of the bending and stresses response of (2D) FG nanobeams to nonlocal length scale, strain gradient microstructure scale, material distribution and geometry.

• Wind and Structures
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• v.27 no.6
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• pp.369-380
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• 2018

In this research work, nonlinear thermal buckling behavior of functionally graded (FG) plates is explored based a new higher-order shear deformation theory (HSDT). The present model has just four unknowns, by using a new supposition of the displacement field which enforces undetermined integral variables. A shear correction factor is, thus, not necessary. A power law distribution is employed to express the disparity of volume fraction of material distributions. Three kinds of thermal loading, namely, uniform, linear, and nonlinear and temperature rises over z-axis direction are examined. The non-linear governing equations are resolved for plates subjected to simply supported boundary conditions at the edges. The results are approved with those existing in the literature. Impacts of various parameters such as aspect and thickness ratios, gradient index, type of thermal load rising, on the non-dimensional thermal buckling load are all examined.

• Structural Engineering and Mechanics
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• v.88 no.4
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• pp.335-354
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• 2023

In this study, analysis of wave propagation characteristics for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates is performed using first-order shear deformation theory (FSDT) and nonlocal strain gradient theory. Uniform distribution (UD) and three types of functionally graded distributions of carbon nanotubes (CNTs) are assumed. The effective mechanical properties of the FG-CNTRC nanoplate are assumed to vary continuously in the thickness direction and are approximated based on the rule of mixture. Also, the governing equations of motion are derived via the extended Hamilton's principle. In numerical examples, the effects of nonlocal parameter, wavenumber, angle of wave propagation, volume fractions, and carbon nanotube distributions on the wave propagation characteristics of the FG-CNTRC nanoplate are studied. As represented in the results, it is clear that the internal length-scale parameter has a remarkable effect on the wave propagation characteristics resulting in significant changes in phase velocity and natural frequency. Furthermore, it is observed that the strain gradient theory yields a higher phase velocity and frequency compared to those obtained by the nonlocal strain gradient theory and classic theory.

• Steel and Composite Structures
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• v.32 no.2
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• pp.281-292
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• 2019

Nonlocal elasticity and Reddy plant theory are used to study the vibration response of functionally graded (FG) nanoplates resting on two parameters elastic medium called Pasternak foundation. Nonlocal higher order theory accounts for the effects of both scale and the effect of transverse shear deformation, which becomes significant where stocky and short nanoplates are concerned. It is assumed that the properties of FG nanoplate follow a power law through the thickness. In addition, Poisson's ratio is assumed to be constant in this model. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of nanoplate with surrounding elastic medium. Using Hamilton's principle, size-dependent governing differential equations of motion and corresponding boundary conditions are derived. A differential quadrature approach is being utilized to discretize the model and obtain numerical solutions for various boundary conditions. The model is validated by comparing the results with other published results.

• Journal of the Korean Society of Safety
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• v.17 no.4
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• pp.31-37
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• 2002

This paper demonstrates the analyses of the interlaminar shear stress of laminated composite plates subjected to transversely impact. For this purpose, a plate finite element model based on the higher order shear deformation plate theory in conjunction with static contact laws is developed. Test materials were CFRP with cross-ply laminate $[O_4/{\theta}_4]_S$, $[90_4/{\theta}_4]_S$ stacking sequences and angle-ply laminate $[{\theta}_4/-{\theta}_4]_S$, $[{\theta}_4/-{\theta}_4]_S$ stacking deguences with $2^t{\times}40^w{\times}100^l(mm)$ dimension. As a result, stacking seguence and fiber orientation were found to have a significant effect on the interlaminar stresses in composite laminates.

• Structural Engineering and Mechanics
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• v.6 no.6
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• pp.583-612
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• 1998

A unified third-order laminate plate theory that contains classical, first-order and third-order theories as special cases is presented. Analytical solutions using the Navier and L$\acute{e}$vy solution procedures are presented. The Navier solutions are limited to simply supported rectangular plates while the L$\acute{e}$vy solutions are restricted to rectangular plates with two parallel edges simply supported and other two edges having arbitrary combination of simply supported, clamped, and free boundary conditions. Numerical results of bending and vibration for a number of problems are discussed in the second part of the paper.