• Advances in nano research
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• 제6권1호
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• pp.21-37
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• 2018

In the present article, wave dispersion behavior of a temperature-dependent functionally graded (FG) nanobeam undergoing rotation subjected to thermal loading is investigated according to nonlocal strain gradient theory, in which the stress numerates for both nonlocal stress field and the strain gradient stress field. The small size effects are taken into account by using the nonlocal strain gradient theory which contains two scale parameters. Mori-Tanaka distribution model is considered to express the gradually variation of material properties across the thickness. The governing equations are derived as a function of axial force due to centrifugal stiffening and displacements by applying Hamilton's principle according to Euler-Bernoulli beam theory. By applying an analytical solution, the dispersion relations of rotating FG nanobeam are obtained by solving an eigenvalue problem. Obviously, numerical results indicate that various parameters such as angular velocity, gradient index, temperature change, wave number and nonlocality parameter have significant influences on the wave characteristics of rotating FG nanobeams. Hence, the results of this research can provide useful information for the next generation studies and accurate deigns of nanomachines including nanoscale molecular bearings and nanogears, etc.

• Structural Engineering and Mechanics
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• 제73권2호
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• pp.191-207
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• 2020

This study aims at investigating the size-dependent free vibration of porous nanoplates when exposed to hygrothermal environment and rested on Kerr foundation. Based on the modified power-law model, material properties of porous functionally graded (FG) nanoplates are supposed to change continuously along the thickness direction. The generalized nonlocal strain gradient elasticity theory incorporating three scale factors (i.e. lower- and higher-order nonlocal parameters, strain gradient length scale parameter), is employed to expand the assumption of second shear deformation theory (SSDT) for considering the small size effect on plates. The governing equations are obtained based on Hamilton's principle and then the equations are solved using an analytical method. The elastic Kerr foundation, as a highly effected foundation type, is adopted to capture the foundation effects. Three different patterns of porosity (namely, even, uneven and logarithmic-uneven porosities) are also considered to fill some gaps of porosity impact. A comparative study is given by using various structural models to show the effect of material composition, porosity distribution, temperature and moisture differences, size dependency and elastic Kerr foundation on the size-dependent free vibration of porous nanoplates. Results show a significant change in higher-order frequencies due to small scale parameters, which could be due to the size effect mechanisms. Furthermore, Porosities inside of the material properties often present a stiffness softening effect on the vibration frequency of FG nanoplates.

• Structural Engineering and Mechanics
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• 제65권5호
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• pp.573-585
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• 2018

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.

• Smart Structures and Systems
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• 제21권4호
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• pp.493-519
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• 2018

This article presents a finite element (FE) model to assess the free vibration and static response of a functionally graded skew magneto-electro-elastic (FGSMEE) plate. Through the thickness material grading of FGSMEE plate is achieved using power law distribution. The coupled constitutive equations along with the total potential energy approach are used to develop the FE model of FGSMEE plate. The transformation matrix is utilized in bringing out the element matrix corresponding to the global axis to a local axis along the skew edges to specify proper boundary conditions. The effect of skew angle on the natural frequency of an FGSMEE plate is analysed. Further, the study includes the evaluation of the static behavior of FGSMEE plate for various skew angles. The influence of skew angle on the primary quantities such as displacements, electric potential, and magnetic potential, and secondary quantities such as stresses, electric displacement and magnetic induction is studied in detail. In addition, the effect of power-law gradient, thickness ratio, boundary conditions and aspect ratio on the free vibration and static response characteristics of FGSMEE plate has been investigated.

• Structural Engineering and Mechanics
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• 제61권2호
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• pp.209-220
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• 2017

The purpose of this paper is to study the geometrically nonlinear free vibration of functionally graded nano/micro beams (FGNBs) based on the modified couple stress theory. For practical applications, some analytical expressions of nonlinear frequencies for FGNBs on a nonlinear Pasternak foundation are developed. Hamilton's principle is employed to obtain nonlinear governing differential equations in the context of both Euler-Bernoulli and Timoshenko beam theories for a comprehensive investigation. The modified continuum theory contains one material length scale parameter to capture the size effect. The variation of two-constituent material along the thickness is modeled using Reddy's power-law. Also, the Mori-Tanaka method as an accurate homogenization technique is implemented to estimate the effective material properties of the FGNBs. The results are presented for both hinged-hinged and clamped-clamped boundary conditions. The nonlinear partial differential equations are reduced to ordinary differential equations using Galerkin method and then the powerful method of homotopy analysis is utilized to obtain the semi-analytical solutions. Eventually, the presented analytical expressions are used to examine the influences of the length scale parameter, material gradient index, and elastic foundation on the nonlinear free vibration of FGNBs.

• Steel and Composite Structures
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• 제21권4호
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• pp.849-862
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• 2016

This paper investigates the static buckling behaviours of Functionally Gradient Polymeric Material (FGPM) shells in the form of hemispherical segment. A new FGPM model based on experimental was considered to investigate the buckling problem of thin-walled spherical shells loaded by the external pressure. The spherical shells were formed by FGPM which was produced adding the two types of graphite powders into epoxy resin. The graphite powders were added to the epoxy resin as volume of 3, 6, 9, and 12%. Halpin-Tsai and Paul models were used to determine the elastic moduli of the parts of FGPM. The detailed static buckling analyses were performed by using finite element method. The influences of the types and volume of graphite powders on the buckling behaviour of the FGPM structures were investigated. The buckling loads of hemispherical FGPM shells based on Halpin-Tsai and Paul models were compared with those determined from the analytical solution of non-graphite condition existing for homogeneous material model. The comparisons between these material models showed that Paul model was overestimated. Besides, the critical buckling loads were predicted. The higher critical buckling loads were estimated for the PV60/65 graphite powder due to the compatible of the PV60/65 graphite powder with resin.

• Corrosion Science and Technology
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• 제2권3호
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• pp.155-160
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• 2003

Plasma spraying technique was used to fabricate functionally graded coating (FGC) of NiCrAIY/YSZ 8wt%$Y_2O_3-ZrO_2$ on a Co-base superalloy (HAYNES 188) substrate. Six layers were coated on the substrate for building up compositionally graded architecture. Conventional thermal barrier coating (TBC) of NiCrAIY/SZ with sharp interface was also fabricated. As-coated FGC and TBC samples were exposed at the temperature of $1100^{\circ}C$ for 10, 50, 100 hours in air. Microstructural change of thermally exposed samples was examined. Pores and microcracks were formed in YSZ layer due to evolution of thermal internal stress at high temperature. The amount of pores and microcracks in YSZ layer were increased with increasing exposure time at high temperature. High temperature oxidation of coatings occurred mainly at the NiCrAIY/YSZ interface. In comparison with the case of TBC. the increased area of the NiCrAIY/YSZ interface in FGC is likely to attribute to forming the higher amount of oxides.

• Smart Structures and Systems
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• 제18권2호
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• pp.267-291
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• 2016

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) sandwich plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present refined theory. The non-linear governing equations are solved for plates subjected to simply supported and clamped boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.

• Advances in materials Research
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• 제5권2호
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• pp.107-120
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• 2016

The static analysis of the simply supported functionally graded plate under transverse load by using a new sinusoidal shear deformation theory based on the neutral surface concept is investigated analytically in the present paper. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. The mechanical properties of the FGM plate are assumed to vary continuously through the thickness according to a power law formulation except Poisson's ratio, which is kept constant. The equilibrium and stability equations are derived by employing the principle of virtual work. Results are provided for thick to thin plates and for different values of the gradient index k, which subjected to sinusoidal or uniformly distributed lateral loads. The accuracy of the present results is verified by comparing it with finite element solution. From the obtained results, it can be concluded that the proposed theory is accurate and efficient in predicting the displacements and stresses of functionally graded plates.

• Steel and Composite Structures
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• 제33권3호
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• pp.463-472
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• 2019

Initial thermo-elastic and steady state creep deformation of a rotating functionally graded simple blade is studied using first-order shear deformation theory. A variable thickness model for cantilever beam has been considered. The blade geometry and loading are defined as functions of length so that one can define his own blade profile and loading using any arbitrary function. The blade is subjected to a transverse distributed load, an inertia body force due to rotation and a distributed temperature field due to a thermal gradient between the tip and the root. All mechanical and thermal properties except Poisson's ratio are assumed to be longitudinally variable based on the volume fraction of reinforcement. The creep behaviour is modelled by Norton's law. Considering creep strains in stress strain relation, Prandtl-Reuss relations, Norton' law and effective stress relation differential equation in term of effective creep strain is established. This differential equation is solved numerically. By effective creep strain, steady state stresses and deflections are obtained. It is concluded that reinforcement particle size and form of distribution of reinforcement has significant effect on the steady state creep behavior of the blade.