• 제목/요약/키워드: linear rule of mixtures

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목재 섬유 복합재(複合材)에 혼합이론(混合理論)의 적용에 관한 연구(硏究)(3) - 유황(硫黃) 화합물(化合物)을 사용한 목재(木材) 섬유(纖維) 복합재(複合材)에 수정된 혼합이론(混合理論)의 상수(常數) 결정(決定) - (The Application of Rule of Mixtures to Fiber-Reinforced Composites(3) - Determination of Constant "a" and "b" for Modified Rule of Mixtures Applied to Fiber-Reinforced, Sulfur-Based Composites -)

  • 이병근
    • Journal of the Korean Wood Science and Technology
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    • 제12권3호
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    • pp.3-8
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    • 1984
  • 섬유의 방향성이 무질서한 composites에 적용되는 Smith와 Cox의 이론(理論)을 포함한 Paul과 Jones의 혼합이론식(混合理論式)은 유황(硫黃) 화합물(化合物)을 사용하여 제조한 목재섬유 복합재(複合材)에도 일차적(一次的)인 liner regression constant가 주어질 때는 사용할 수가 있음을 보여준다. $E_c=\frac{1}{3}aE_fV_f+bE_mV_m$으로 표시된 이 liner regression from에 math. rom pack을 사용한 Hewlett Packard 75C(HP 75C) computer의 계산 결과는 목재 섬유 복합재(複合材)에 사용된 matrix의 종류, 섬유판의 밀도와 목재 밑 목질 섬유의 종류에 관계없이 a=3.27~3.54와 b=-2.47~-2.80의 일정한 범위의 값을 보여주므로, 지금까지 무(無)질서한 방향성을 지닌 장(長)섬유로 된 복합재(複合材)에만 적용되어 왔던 Paul과 Jones의 혼합이론(混合理論)과 이것과 같은 방향을 지닌 단(短) 섬유로 된 목재(木材)나 목질(木質) 섬유 composites에도 적용될 수 있음을 증명하고 있다.

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이중 후방 응력 경화 모델을 이용한 주기 하중에서의 래쳐팅 거동 현상 연구 (Simulation of Ratcheting Behavior under Stress Controlled Cyclic Loading using Two-Back Stress Hardening Constitutive Relation)

  • 홍성인;황두순;윤수진
    • 소성∙가공
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    • 제17권1호
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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.

기능경사재를 위한 균질화와 이산화-미시역학 모델에 대한 비교 수치해석 (Comparative Numerical Analysis of Homogenized and Discrete-Micromechanics Models for Functionally Graded Materials)

  • 하대율;이홍우;조진래
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2000년도 춘계학술대회논문집A
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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.

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평판 표면에서 HFC32/HFC152a 혼합냉매의 풀 비등 열전달계수 (Pool Boiling Heat Transfer Coefficient of HFC32/HFC152a on a Plain Surface)

  • 강동규;이요한;정동수
    • 설비공학논문집
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    • 제25권9호
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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.

혼합냉매의 풀비등 열전달 상관식 (Pool Boiling Heat Transfer Correlation for Mixture Refrigerants)

  • 고영환;김종곤;박진석;정동수;김영일
    • 설비공학논문집
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    • 제13권2호
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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.

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기능경사 소재 등가 물성치 예측을 위한 균질화 기법의 특성분석을 위한 수치해석 (Numerical Analysis for the Characteristic Investigation of Homogenization Techniques Used for Equivalent Material Properties of Functionally Graded Material)

  • 조진래;최주형;신대섭
    • 한국전산구조공학회논문집
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    • 제21권1호
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    • pp.13-20
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    • 2008
  • 기능경사 소재(FGM)에는 서로 다른 두 가지 구성입자들이 혼합되어 있는 경사층(graded layer)이 삽입되어, 소재 전 영역에 걸쳐 구성입자의 체적분율이 연속적이고 기능적으로 변화하도록 되어있다. 이러한 이상(dual-phase) 입자복합재의 열 기계적 거동을 해석함에 있어 필수적인 경사층의 물성치는 전통적으로 균질화 기법을 이용하여 예측되었다. 하지만, 이러한 균질화 기법은 구성입자의 형태, 분산구조 등과 같은 상세 형상을 반영하지 못하지 때문에 복합재의 총체적인 등가 물성치 예측에만 국한 되어왔다. 이러한 맥락에서 본 연구에서는 경사층을 미시역학적으로 이산화 모델링하고, 다양한 체적분율과 외부 하중조건에 대해 유한요소해석을 실시하여 이러한 균질화 기법들의 특성을 분석하였다.

경사기능재료 판의 최적설계 (Optimal Design of Functionally Graded Plates)

  • 나경수;김지환
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2006년도 춘계학술대회논문집
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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.

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On thermally induced instability of FG-CNTRC cylindrical panels

  • Hashemi, Razieh;Mirzaei, Mostafa;Adlparvar, Mohammad R.
    • Advances in nano research
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    • 제10권1호
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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.

Nonlinear vibration of FG-CNTRC curved pipes with temperature-dependent properties

  • Mingjie Liu;Shaoping Bi;Sicheng Shao;Hadi Babaei
    • Steel and Composite Structures
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    • 제46권4호
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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.

On vibration and flutter of shear and normal deformable functionally graded reinforced composite plates

  • Abdollahi, Mahdieh;Saidi, Ali Reza;Bahaadini, Reza
    • Structural Engineering and Mechanics
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    • 제84권4호
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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.