• Journal of the Korean Wood Science and Technology
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• v.12 no.3
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• pp.3-8
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• 1984

It is shown that Paul and Jones' Rule of Mixtures modified by Smith and Cox's theory can be used for the fiber-reinforced, sulfur-based composites, when the constant for the linear regression equation is given. The computation results, programmed by Hewlett Packard 75C (HP 75C) using math rom pack for the linear regression form, expressed as $E_c=\frac{1}{3}aE_fV_f+bE_mV_m$, turn out to be a=3.27-3.54 b=-2.47~-2.80. This results indicate that the factors such as density of fiber mat and the amount of matrix used have nothing for affecting the numerical value of the constants a and b of the linear regression form. Conclusively this results also show that the Paul and Jones' Rule of Mixtures which has been used for the composites made by randomly-oriented long fiber can also be used for the composites made by short fiber with the same fiber orientation such as wood and lignocellulosic fibers.

• Transactions of Materials Processing
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• v.17 no.1
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• pp.19-26
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• 2008

In the present work, the ratcheting behavior under uniaxial cyclic loading is analyzed. A comparison between the published and the results from the present model is also included. In order to simulate the ratcheting behavior, Two-Back Stress model is proposed by combining the non-linear Armstrong-Frederick rule and the non-linear Phillips hardening rule based on kinematic hardening equation. It is shown that some ratcheting behaviors can be obtained by adjusting the control material parameters and various evolutions of the kinematic hardening parameter can be obtained by means of simple combination of hardening rules using simple rule of mixtures. The ultimate back stress is also derived for the present combined kinematic hardening models.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.399-404
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• 2000

Functionally graded materials(FGMs) involve dual-phase graded layers in which two different constituents are mixed continuously and functionally according to a given volume fraction. For the analysis of their thermo-mechanical response, conventional homogenized methods have been widely employed in order to estimate equivalent material properties of the graded layer. However, such overall estimations are insufficient to accurately predict the local behavior. In this paper, we compare the thermo-elastic behaviors predicted by several overall material-property estimation techniques with those obtained by discrete analysis models utilizing the finite element method, for various volume fractions and loading conditions.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.25 no.9
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• pp.484-492
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• 2013

Nucleate pool boiling heat transfer coefficients (HTCs) are measured with HFC32/HFC152a mixture at several compositions. All data are taken at the liquid pool temperature of $7^{\circ}C$, on a horizontal plain square surface of $9.53{\times}9.53$ mm, with heat fluxes of 10 $kW/m^2$ to 100 $kW/m^2$ with an interval of 10 $kW/m^2$, in the increasing order of heat flux. Test results show that the HTCs of these mixtures are up to 45% lower than those of the ideal HTCs calculated by a linear mixing rule with pure fluids' HTCs, due to the mass transfer resistance associated with non-azeotropic refrigerant mixtures. Pool boiling data show the deduction in HTCs with an increase in GTD of the mixture. The present mixture data agree well with five well known correlations, within 20% deviation.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.13 no.2
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• pp.122-133
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• 2001

Pool boiling heat transfer coefficients(HTCs) of HFC32/HFC134a, HFC125/HFC134a, HFC32/HFC125 and HFC32/HFC125/HFC134a were measured on a horizontal smooth tube. The experimental apparatus was specially designed to simulate the real heat transfer tube with the use of the secondary fluid of water. Data were taken in the order of decreasing heat flux starting at 80kW/$m^2\; and\; ending\; at\; 5kW/m^2$ in the pool temperature at $7^{\circ}C$. Test results showed that HTCs of these mixtures were 11~38% lower than those of ideal HTCs calculated by a linear mixing rule with pure fluids、 HTCs. Experimental data were compared with Stephan & Korner, Thome, Schlunder, Thome & Shakir、s correlations only to find that those correlations were not satisfactory for all fluids. Hence, a new correlation based on the present data was proposed which could be applied even to the ternary mixture. The correlation predicts the degradation of HTCs of mixtures well, showing a mean deviation of less than 15% for all the mixture data.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.1
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• pp.13-20
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• 2008

Graded layers in which two different constituent particles are mixed are inserted into functionally graded material such that the volume fractions of constituent particles vary continuously and functionally over the entire material domain. The material properties of this dual-phase graded region, which is essential for the numerical analysis of the thermo-mechanical behavior of FGM, have been predicted by traditional homogenization methods. But, these methods are limited to predict the global equivalent material properties of FGMs because the detailed geometry information such as the particel shape and the dispersion structure is not considered. In this context, this study intends to investigate the characteristics of these homogenization methods through the finite element analysis utilizing the discrete micromechanics models of the graded layer, for various volume fractions and external loading conditions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1061-1064
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• 2006

Optimal design of functionally graded plates is investigated considering stress and critical temperature. Material properties are assumed to be temperature dependent and varied continuously in the thickness direction. The effective material properties are obtained by applying linear rule of mixtures. The 3-D finite element model is adopted using an 18-node solid element to analyze more accurately the variation of material properties and temperature field in the thickness direction. For stress analysis, the tensile stress ratio and compressive stress ratio of the structure under mechanical load are investigated. In the thermo-mechanical buckling analysis, temperature at each node is obtained by solving the steady-state heat transfer problem and Newton-Raphson method is used for material nonlinear analysis. Finally, the optimal design of FGM plates is studied for stress reduction and improving thermo-mechanical buckling behavior, simultaneously.

• Advances in nano research
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• v.10 no.1
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• pp.43-57
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• 2021

In this study, thermally induced bifurcation buckling of shallow composite cylindrical panels reinforced with aligned single-walled carbon nanotubes is investigated. Distribution of carbon nanotubes across the thickness of the cylindrical panel as reinforcements may be either uniform or functionally graded. Thermo-mechanical properties of the matrix and reinforcements are considered to be temperature dependent. Properties of the cylindrical panel are obtained using a refined micromechanical approach which introduces the auxiliary parameters into the rule of mixtures. The governing equations are obtained by using the static version of the Hamilton principle based on the first-order shear deformation theory and considering the linear strain-displacement relation. An energy-based Ritz method and an iterative process are used to obtain the critical buckling temperature of composite cylindrical panel with temperature dependent material properties. In addition, the effect of various parameters such as the boundary conditions, different geometrical conditions, distribution pattern of CNTs across the thickness and their volume fraction are studied on the critical buckling temperature and buckled pattern of cylindrical panels. It is shown that FG-X type of CNT dispersion is the most influential type in thermal stability.

• Steel and Composite Structures
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• v.46 no.4
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• pp.553-563
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• 2023

In the current research, the nonlinear free vibrations of curved pipes made of functionally graded (FG) carbon nanotube reinforced composite (CNTRC) materials are investigated. It is assumed that the FG-CNTRC curved pipe is supported on a three-parameter nonlinear elastic foundation and is subjected to a uniform temperature rise. Properties of the curved nanocomposite pipe are distributed across the radius of the pipe and are given by means of a refined rule of mixtures approach. It is also assumed that all thermomechanical properties of the nanocomposite pipe are temperature-dependent. The governing equations of the curved pipe are obtained using a higher order shear deformation theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the pipe. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large deflection in the curved nanocomposite pipe. For the case of nanocomposite curved pipes which are simply supported in flexure and axially immovable, the motion equations are solved using the two-step perturbation technique. The closed-form expressions are provided to obtain the small- and large-amplitude frequencies of FG-CNTRC curved pipes rested on a nonlinear elastic foundation in thermal environment. Numerical results are given to explore the effects of CNT distribution pattern, the CNT volume fraction, thermal environment, nonlinear foundation stiffness, and geometrical parameters on the fundamental linear and nonlinear frequencies of the curved nanocomposite pipe.

• Structural Engineering and Mechanics
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• v.84 no.4
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• pp.437-452
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• 2022

For the first time, the higher-order shear and normal deformable plate theory (HOSNDPT) is used for the vibration and flutter analyses of the multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) plates under supersonic airflow. For modeling the supersonic airflow, the linear piston theory is adopted. In HOSNDPT, Legendre polynomials are used to approximate the components of the displacement field in the thickness direction. So, all stress and strain components are encountered. Either uniform or three kinds of non-uniform distribution of graphene platelets (GPLs) into polymer matrix are considered. The Young modulus of the FG-GPLRC plate is estimated by the modified Halpin-Tsai model, while the Poisson ratio and mass density are determined by the rule of mixtures. The Hamilton's principle is used to obtain the governing equations of motion and the associated boundary conditions of the plate. For solving the plate's equations of motion, the Galerkin approach is applied. A comparison for the natural frequencies obtained based on the present investigation and those of three-dimensional elasticity theory shows a very good agreement. The flutter boundaries for FG-GPLRC plates based on HOSNDPT are described and the effects of GPL distribution patterns, the geometrical parameters and the weight fraction of GPLs on the flutter frequencies and flutter aerodynamic pressure of the plate are studied in detail. The obtained results show that by increasing 0.5% of GPLs into polymer matrix, the flutter aerodynamic pressure increases approximately 117%, 145%, 166% and 196% for FG-O, FG-A, UD and FG-X distribution patterns, respectively.