• 제목/요약/키워드: rule of mixtures

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Nonlinear free vibration of FG-CNT reinforced composite plates

  • Mirzaei, Mostafa;Kiani, Yaser
    • Structural Engineering and Mechanics
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    • 제64권3호
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    • pp.381-390
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    • 2017
  • Present paper deals with the large amplitude flexural vibration of carbon nanotube reinforced composite (CNTRC) plates. Distribution of CNTs as reinforcements may be uniform or functionally graded (FG). The equivalent material properties of the composite media are obtained according to a refined rule of mixtures which contains efficiency parameters. To account for the large deformations, von $K{\acute{a}}rm{\acute{a}}n$ type of geometrical nonlinearity is included into the formulation. The matrix representation of the governing equations is obtained according to the Ritz method where the basic shape functions are written in terms of the Chebyshev polynomials. Time dependency of the problem is eliminated by means of the Galerkin method and the resulting nonlinear eigenvalue problem is solved employing a direct displacement control approach. Results are obtained for completely clamped and completely simply supported plates. Results are first validated for the especial cases of FG-CNTRC and cross-ply laminated plates. Afterwards, parametric studies are given for FG-CNTRC plates with different boundary conditions. It is shown that, nonlinear frequencies are highly dependent to the volume fraction and dispersion profiles of CNTs. Furthermore, mode redistribution is observed in both simply supported and clamped FG-CNTRC plates.

액체혼합물의 밀도 측정과 3차 상태방정식에 의한 과잉 몰부피의 예측 (Density Measurement of Liquid Mixture and Estimation of Excess Molar Volume by A Cubic Equation of State)

  • 김정민;배효광
    • Korean Chemical Engineering Research
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    • 제43권5호
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    • pp.637-640
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    • 2005
  • 극성과 비극성의 물질인 methyl tert-butyl ether(MTBE)와 2,2,4-trimethylpentane 혼합물과 methyl ethyl ketone(MEK)와 2,2,4-trimethylpentane 2성분의 액체혼합물 그리고 극성의 물질인 MTBE과 MEK 2성분 액체혼합물의 밀도를 densitometer를 사용하여 278.15 K, 288.15 K, 298.15 K에서 각각 측정하였다. 측정한 밀도로부터 얻은 2성분계 과잉몰부피의 측정값과 Huron-Vidal의 혼합법칙을 사용한 Peng-Robinson-Stryjek-Vera(PRSV)의 3차 상태방정식으로부터 계산한 계산값이 잘 일치하였으며 극성물질을 포함한 혼합물의 몰부피 계산에 3차의 PRSV 상태방정식이 이용될 수 있음을 확인하였다.

Filament winding에 의해 제조된 복합재료 NOL RING시험편의 최적 인장강도 평가법에 관한 연구 (A Study on the Optimum Evaluation Method for Tensile NOL Ring Specimen Manufactured by Filament Winding Process)

  • 권순철;임철문;배창원;엄수현;김윤해
    • 한국복합재료학회:학술대회논문집
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    • 한국복합재료학회 2000년도 추계학술발표대회 논문집
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    • pp.203-207
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    • 2000
  • Filament Winding Process is a comparatively simple operation in which continuous reinforcements in the form of roving are wound over a rotating mandrel. And now well established as a versatile method for storage tanks and pipe for the chemical and other industries . In this study, tensile strength of a filament wound ring specimens were evaluated by split disk test fixture and dress disk test fixture , The results obtained from experiments were compared with the theoretical values obtained by the rule of mixtures. And the purpose of this paper is the suggestion of an appropriate test method for the evaluation of tensile properties of filament wound structures .The tensile strength of a ring specimen tested by the dress disk test showed better agreement with the theoretical values than of a ring specimen tested by the split disk test because the stress concentration in edges of a split disk test fixture is more severe than that of dress disk test fixture. The results showed that the tensile strength of a ring specimen was influenced by the geometry of test fixture, the continuity of fibers, fiber-tension, fiber-end and stress concentration in specimen.

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Free vibration analysis of FG composite plates reinforced with GPLs in thermal environment using full layerwise FEM

  • Mohammad Sadegh Tayebi;Sattar Jedari Salami;Majid Tavakolian
    • Structural Engineering and Mechanics
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    • 제85권4호
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    • pp.445-459
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    • 2023
  • The current investigation is the first endeavor to apply the full layerwise finite element method (FEM) in free vibration analysis of functionally graded (FG) composite plates reinforced with graphene nanoplatelets (GPLs) in thermal environment. Unlike the equivalent single-layer (ESL) theories, the layerwise FEM focuses on all three-dimensional (3D) effects. The GPLs weight fraction is presumed invariable in each layer but varies through the plate thickness in a layerwise model. The modified Halpin-Tsai model is employed to acquire the effective Young's modulus. The rule of mixtures is applied to specify the effective Poisson's ratio and mass density. First, the current method is validated by comparing the numerical results with those stated in the available works. Next, a thorough numerical study is performed to examine the influence of various factors involving the pattern of distribution, weight fraction, geometry, and size of GPLs, together with the thickness-to-span ratio, thermal environment, and boundary conditions of the plate, on its free vibration behaviors. Numerical results demonstrate that employing a small percentage of GPL as reinforcement considerably grows the natural frequencies of the pure epoxy. Also, distributing more square-shaped GPLs, involving a smaller amount of graphene layers, and vicinity to the upper and lower surfaces make it the most efficient method to enhance the free vibration behaviors of the plate.

취성기지 복합재료의 물성치에 미치는 계면분리의 영향 (Effect of Interfacial Debonding on the Material Properties of Brittle Matrix Composites)

  • 염영진;진민철
    • Composites Research
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    • 제16권1호
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    • pp.42-49
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    • 2003
  • 취성기지 복합재료는 섬유와 기지 사이에 계면분리가 존재하는 경우가 있는데 이것은 복합재료의 강도와 강성저하의 원인이 된다. 계면분리와 섬유체적비가 복합재료의 기계적 물성치에 미치는 영향에 대만 유한요소해석을 수행하였다. 우선 몇 가지 가정하에 복합재료를 구성하는 섬유와 기지에 대하여 간단하게 모델링하고 이웃하는 대표체적요소의 경계를 따라 응력과 변위 연속조건을 부과하였다. 강성상수들을 역변환하여 복합재료의 유효물성치를 구하였다. 완전접착의 경우 수치해를 혼합물법칙에 의한 이론해와 비교한 결과 일치함을 알 수 있었고 계면분리가 큰 경우 섬유체적비가 증가하더라도 물성치가 감소함을 알 수 있었다.

Processing and mechanical property evaluation of maize fiber reinforced green composites

  • Dauda, Mohammed;Yoshiba, Masayuki;Miura, Kazuhiro;Takahashi, Satoru
    • Advanced Composite Materials
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    • 제16권4호
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    • pp.335-347
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    • 2007
  • Green composites composed of long maize fibers and poly $\varepsilon$-caprolactone (PCL) biodegradable polyester matrix were manufactured by the thermo-mechanical processing termed as 'Sequential Molding and Forming Process' that was developed previously by the authors' research group. A variety of processing parameters such as fiber area fraction, molding temperature and forming pressure were systematically controlled and their influence on the tensile properties was investigated. It was revealed that both tensile strength and elastic modulus of the composites increase steadily depending on the increase in fiber area fraction, suggesting a general conformity to the rule of mixtures (ROM), particularly up to 55% fiber area fraction. The improvement in tensile properties was found to be closely related to the good interfacial adhesion between the fiber and polymer matrix, and was observed to be more pronounced under the optimum processing condition of $130^{\circ}C$ molding temperature and 10 MPa forming pressure. However, processing out of the optimum condition results in a deterioration in properties, mostly fiber and/or matrix degradation together with their interfacial defect as a consequence of the thermal or mechanical damages. On the basis of microstructural observation, the cause of strength degradation and its countermeasure to provide a feasible composite design are discussed in relation to the optimized process conditions.

3-메틸펜테인과 에틸렌 글리콜 모노프로필 에테르 및 에틸렌 글리콜 아이소프로필 에테르 혼합물에 대한 2성분계 등온 기-액 상 평형 (Isothermal Vapor-liquid Equilibria for the Binary Mixtures of 3-Methylpentane with Ethylene Glycol Monopropyl Ether and Ethylene Glycol Isopropyl Ether)

  • 형성훈;장성현;김화용
    • Korean Chemical Engineering Research
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    • 제53권3호
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    • pp.302-308
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    • 2015
  • 본 연구에서는 3-Methylpentane을 포함하는 Ethylene glycol monopropyl ether ($C_3E_1$) 및 Ethylene glycol isopropyl ether ($iC_3E_1$) 계면활성제 혼합물에 대한 2성분계 기-액 상 평형을 서로 다른 온도 조건(303.15, 318.15, 333.15K)에서 측정 및 비교하였다. $C_3E_1$은 분자 내 수소결합과 분자 간 수소결합이 동시에 나타나는 자가 회합 성 물질이므로 상 평형 예측을 어렵게 하는 경향이 있다. 본 연구의 목적은 $C_3E_1$ 혼합물과 그 이성질체인 $iC_3E_1$ 혼합물의 상 평형을 각각 측정 및 비교함으로써, 자가 회합 성 물질의 이성질체가 상 평형에 어떠한 영향을 미치는지 알아보는 것이다. 측정된 시스템은 PR-WS-NRTL, PR-WS-UNIQUAC, 그리고 PR-WS-WILSON 모델을 이용하여 각각 계산하고 각 모델의 성능을 비교하였다. 계산에 사용된 모델은 대부분 좋은 결과를 보여주었으며, 특히 PR-WS-NRTL 모델이 가장 좋은 결과를 나타냈다. 또한 측정 시스템 간의 상 평형 차이가 크게 발생하지 않은 것으로 보아 자가 회합 성 물질의 이성질체가 상 평형에 끼치는 영향은 크지 않음을 알 수 있었다.

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.

목재 섬유 복합재(複合材)에 혼합이론(混合理論)의 적용에 관(關)한 연구(硏究) (1) - 유황(硫黃) 화합물(化合物)을 사용한 목재(木材) 섬유(纖維) 복합재(複合材)의 기계적 성질(性質) - (The Application of Rule of Mixtures to Fiber-Reinforced Composites(1) - Mechanical Properties of Fiber-Reinforced, Sulfur-Based Composites -)

  • 이병근
    • Journal of the Korean Wood Science and Technology
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    • 제11권3호
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    • pp.3-13
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    • 1983
  • 크라프트 펄프의 screening rejects, 볏짚 그리고 이들의 1 : 1 비율의 혼합 물질을 사용하여, 5가지의 다른 섬유판(纖維板) 밀도(密度)를 가지는 섬유판을 만들었다. 이들을 유황(硫黃) 화합물(化合物)에 침적(沈積)시켰다. 제조(製造)한 복합재(複合材) 속의 유황(硫黃) 화합물(化合物)의 노화효과(老化效果)를 관찰하기 위해 1년동안 일정한 시간(時間) 간격(間隔)으로, 이 복합재의 기계적 강도(强度)를 Young 계수(係數)로 나타내었다. 최적(最適)의 섬유판과 유황 화합물의 제조 조건하(下)에서, 이 목재(木材) 섬유(纖維) 복합재(複合材)의 Young 계수(係數)는 기존의 합성수지로 만든 복합재나 목재 선유로 만든 집성재(集成材)나 복합재보다 훨씬 큰 결과를 보여 주었다. 예를 들어, 목재 섬유판 밀도가 0.35gm/$cm^3$인 이 복합재의 modulus of elasticity와 modulus of rupture는 각각 1,000,000psi와 7000psi인데 반해, 섬유판 밀도가 1.28gm/$cm^3$인 hardboard의 그것들은 각각 800,000psi와 6000psi를 나나내었다.

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Vibration behavior of trapezoidal sandwich plate with functionally graded-porous core and graphene platelet-reinforced layers

  • Liang, Di;Wu, Qiong;Lu, Xuemei;Tahouneh, Vahid
    • Steel and Composite Structures
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    • 제36권1호
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    • pp.47-62
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    • 2020
  • In this study, free vibration behavior of trapezoidal sandwich plates with porous core and two graphene platelets (GPLs) reinforced nanocomposite outer layers are presented. The distribution of pores and GPLs are supposed to be functionally graded (FG) along the thickness of core and nanocomposite layers, respectively. The effective Young's modulus of the GPL-reinforced (GPLR) nanocomposite layers is determined using the modified Halpin-Tsai micromechanics model, while the Poisson's ratio and density are computed by the rule of mixtures. The FSDT plate theory is utilized to establish governing partial differential equations and boundary conditions (B.C.s) for trapezoidal plate. The governing equations together with related B.C.s are discretized using a mapping- generalized differential quadrature (GDQ) method in the spatial domain. Then natural frequencies of the trapezoidal sandwich plates are obtained by GDQ method. Validity of current study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns of two faces through the thickness, porosity coefficient and distribution of porosity on natural frequencies characteristics. New results show the importance of this permeates on vibrational characteristics of porous/GPLR nanocomposite plates. Finally, the influences of B.C.s and dimension as well as the plate geometry such as face to core thickness ratio on the vibration behaviors of the trapezoidal plates are discussed.