• Steel and Composite Structures
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• 제52권3호
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• pp.273-291
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• 2024

This paper presents a three-dimensional displacement-based formulation to investigate the free vibration of functionally graded nanoplates resting on a Winkler-Pasternak foundation based on the nonlocal elasticity theory. The material properties of the FG nanoplate are considered to vary continuously through the thickness of the nanoplate according to the power-law distribution model. A general three-dimensional displacement field is considered for the plate, which takes into account the out-of-plane strains of the plate as well as the in-plane strains. Unlike the shear deformation theories, in the present formulation, no predetermined form for the distribution of displacements and transverse strains is considered. The equations of motion for functionally graded nanoplate are derived based on Hamilton's principle. The solution is obtained for simply-supported nanoplate, and the predicted results for natural frequencies are compared with the predictions of shear deformation theories which are available in the literature. The predictions of the present theory are discussed in detail to investigate the effects of power-law index, length-to-thickness ratio, mode numbers and the elastic foundation on the dynamic behavior of the functionally graded nanoplate. The present study presents a three-dimensional solution that is able to determine more accurate results in predicting of the natural frequencies of flexural and thickness modes of nanoplates. The effects of parameters that play a key role in the analysis and mechanical design of functionally graded nanoplates are investigated.

• Geomechanics and Engineering
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• 제12권1호
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• pp.9-34
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• 2017

In this work, an efficient and simple quasi-3D hyperbolic shear deformation theory is developed for bending and vibration analyses of functionally graded (FG) plates resting on two-parameter elastic foundation. The significant feature of this theory is that, in addition to including the thickness stretching effect, it deals with only 5 unknowns as the first order shear deformation theory (FSDT). The foundation is described by the Pasternak (two-parameter) model. The material properties of the plate are assumed to vary continuously in the thickness direction by a simple power law distribution in terms of the volume fractions of the constituents. Equations of motion for thick FG plates are obtained within the Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The numerical results are given in detail and compared with the existing works such as 3-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates resting on elastic foundation.

• Journal of the Korean Wood Science and Technology
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• 제35권5호
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• pp.7-15
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• 2007

To evaluate the durability of finger-jointed woods according to change of humidity conditions, four types of finger-jointed woods glued with different kinds of adhesives and finger pitches were made with Sitka spruce, and the effect of humidity conditions on creep performances was investigated. The shape of creep curves differed among humidity conditions, and the inclination of creep curves was greatest in 85%RH, and lowest in 65%RH. Their creep curves showed a linear behavior beyond approximately one hour, regardless of humidity conditions. The A values of the creep curves fitted to power law increased with increasing relative humidity, whereas the A' values were in order of 30 > 85 > 65%RH unlike the A values. The initial deformation increased with increasing relative humidity, whereas the creep deformation unlike the initial deformation was in order of 85 > 30 > 65%RH, and it was found that the creep deformation of finger-jointed woods indicated the smaller amount in air-dry moisture content rather than in a low moisture content less than 30%RH. Finger-jointed woods with 6.8 mm (L) pitch had the greater creep amount than in those with 4.4 mm (S) pitch in all humidity conditions. The difference of creep amount between both adhesives in all humidity conditions was small. Relative creep at 240 hr was greatest as 62.2~71.9% in 85%RH, and the values indicated 2.1~2.6 times that of 30%RH and 3.0~3.6 times that of 65%RH and were equal or slightly greater than that of solid spruce.

• Journal of the Korean Wood Science and Technology
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• 제45권6호
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• pp.689-702
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• 2017

In this study, with the view to using effectively small and medium diameter Korean domestic woods as structural materials, cross-laminated woods were manufactured by using six species of Korean domestic softwoods and hardwoods, and bending creep properties were investigated for each species. The creep curves showed the shape of the exponential function plot, and the creep curves after 1 hour were able to estimate by fitting it to the power law. The initial and creep compliances of cross-laminated woods showed the higher values in wood species with a low density than in that with a high density. And by cross-laminating, the initial and creep compliances perpendicular to the grain considerably decreased, the extent of the decrease was found to be greater in creep deformation than in initial deformation. The creep anisotropies of cross-laminated woods were considerably decreased by cross-laminating. The relative creep of $C_{\bot}$ type composed of perpendicular-direction lamina in the faces decreased 0.59 - 0.64 times compared to that of $P_{\bot}$ type composed of perpendicular-direction laminae in all layers, and that for $C_{\parallel}$ type composed of parallel-direction laminae in the faces increased 1.5 - 1.6 times compared to that of $P_{\parallel}$ type composed of parallel-direction laminae in all layers.

• Earthquakes and Structures
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• 제13권3호
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• pp.255-265
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• 2017

In this paper, an efficient shear deformation theory is developed for wave propagation analysis in a functionally graded beam. More particularly, porosities that may occur in Functionally Graded Materials (FGMs) during their manufacture are considered. The proposed shear deformation theory is efficient method because it permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents; but the rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The governing equations of the wave propagation in the functionally graded beam are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded beam is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions, the depth of beam, the number of wave and the porosity on wave propagation in functionally graded beam are discussed in details. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded beam.

• 동력기계공학회지
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• 제9권4호
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• pp.96-101
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• 2005

Magnesium alloys have been widely used for many structural components of automobiles and aircraft because of high specific strength and good cast ability in spite of hexagonal closed-packed crystal structure of pure magnesium. In this study, uniaxial tension tests at high temperature and creep tests are done in order to investigate the characteristics of high temperature and mechanisms for creep deformation of AZ31 Mg alloy. Yield stress and ultimate tensile stress decreased with increasing temperature, but elongation increased from results of uniaxial tension test at high temperature. The apparent activation energy Qc, the applied stress exponent n and rupture life have been determined during creep of AZ31 Mg alloy over the temperature range of 473K to 573K and stress range of 23.42 MPa to 93.59 MPa, respectively, in order to investigate the creep behavior. Constant load creep tests were carried out in the equipment including automatic temperature controller, whose data are sent to computer. At around the temperature of $473K{\sim}493K$ and under the stress level of $62.43{\sim}93.59%MPa$, and again at around the temperature of $553K{\sim}573K$ and under the stress level of $23.42{\sim}39.00MPa$, the creep behavior obeyed a simple power-law relating steady state creep rate to applied stress and the activation energy for the creep deformation was nearly equal, respectively, and a little low to that of the self diffusion of Mg alloy including aluminum. Also rupture surfaces at high temperature have had bigger dimples than those at lower temperature by SEM.

• 한국금형공학회:학술대회논문집
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• 한국금형공학회 2008년도 하계 학술대회
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• pp.39-44
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• 2008

Magnesium alloys have given high attention to the industry of light-weigh as automobile and electronics with aluminium, titanium and composite alloys due to their high strength, low specific density and good damping characteristics. But the magnesium contained structures under high temperature have the problems related to creep deformation and rupture life, which is a reason of developing the new material against creep deformation to use them safely. The purpose of this study is to predict the creep deformation mechanism and rupture time of AZ31 magnesium alloy. For this, creep tests of AZ31 magnesium alloy were done under constant creep load and temperature with the equipment including automatic temperature controller with acquisition computer. The apparent activation energy Qc and the applied stress exponent n, rupture life have been determined during creep of AZ31 Mg alloy over the temperature range of $150^{\circ}C$ to $300^{\circ}C$. In order to investigate the creep behavior. Constant load creep tests were carried out in the equipment including automatic temperature controller, whose data are sent to computer. At around the temperature of $150^{\circ}C{\sim}300^{\circ}C$ the creep behavior obeyed a simple power-law relating steady state creep rate to applied stress and the activation energy for the creep deformation was nearly equal and a little low, respectively, to that of the self diffusion of Mg alloy.

• Coupled systems mechanics
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• 제9권3호
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• pp.237-264
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• 2020

This article investigates the static behaviour of functionally graded (FG) plates sometimes declared as advanced composite plates by using a simple and accurate quasi-3D and 2D hyperbolic higher-order shear deformation theories. The properties of functionally graded materials (FGMs) are assumed to vary continuously through the thickness direction according to exponential law distribution (E-FGM). The kinematics of the present theories is modeled with an undetermined integral component and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate; therefore, it does not require the shear correction factor. The fundamental governing differential equations and boundary conditions of exponentially graded plates are derived by employing the static version of principle of virtual work. Analytical solutions for bending of EG plates subjected to sinusoidal distributed load are obtained for simply supported boundary conditions using Navier'is solution procedure developed in the double Fourier trigonometric series. The results for the displacements and stresses of geometrically different EG plates are presented and compared with 3D exact solution and with other quasi-3D and 2D higher-order shear deformation theories to verify the accuracy of the present theory.

• Geomechanics and Engineering
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• 제22권5호
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• pp.415-431
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• 2020

In this study, dynamics responses of advanced composite plates resting variable elastic foundations via a quasi-3D theory are developed using an analytical approach. This higher shear deformation theory (HSDT) is included the shear deformation theory and effect stretching that has five unknowns, which is even inferior to normal deformation theories found literature and other theories. The quasi-three-dimensional (quasi-3D) theory accounts for a parabolic distribution of the transverse shear deformation and satisfies the zero traction boundary conditions on the surfaces of the advanced composite plate without needing shear correction factors. The plates assumed to be rest on two-parameter elastic foundations, the Winkler parameter is supposed to be constant but the Pasternak parameter varies along the long side of the plate with three distributions (linear, parabolic and sinusoidal). The material properties of the advanced composite plates gradually vary through the thickness according to two distribution models (power law and Mori-Tanaka). Governing differential equations and associated boundary conditions for dynamics responses of the advanced composite plates are derived using the Hamilton principle and are solved by using an analytical solution of Navier's technique. The present results and validations of our modal with literature are presented that permitted to demonstrate the accuracy of the present quasi-3D theory to predict the effect of variables elastic foundation on dynamics responses of advanced composite plates.

• Steel and Composite Structures
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• 제39권1호
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• pp.51-64
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• 2021

This paper presents a high-order shear and normal deformation theory for the bending of FGM plates. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. Based on the novel shear and normal deformation theory, the position of neutral surface is determined and the governing equilibrium equations based on neutral surface are derived. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Navier-type analytical solution is obtained for functionally graded plate subjected to transverse load for simply supported boundary conditions. The accuracy of the present theory is verified by comparing the obtained results with other quasi-3D higher-order theories reported in the literature. Other numerical examples are also presented to show the influences of the volume fraction distribution, geometrical parameters and power law index on the bending responses of the FGM plates are studied.