• Journal of Mechanical Science and Technology
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• 제20권11호
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• pp.1891-1897
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• 2006

In this study, a new model to predict the effective elastic constants of composites with spherical fillers is proposed. The original Eshelby model is extended to a finite filler volume fraction without using Mori-Tanaka's mean field approach. When single filler is embedded in the matrix, the effective elastic constants of the composite are computed. The composite is in turn considered as a new matrix, where new single filler is again embedded in the matrix. The predicted results by the present model with a series of embedding procedures are compared with those by Mori-Tanaka, self-consistent, and generalized self-consistent models. It is revealed through parametric studies such as stiffness ratio of the filler to the matrix and filler volume fraction that the present model gives more accurate predictions than Mori-Tanaka model without using the complicated numerical scheme used in self-consistent and generalized self-consistent models.

• Composites Research
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• 제17권6호
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• pp.8-13
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• 2004

Eshelby의 등가개재물범과 Mori-Tanaka의 평균장 이론을 이용하여 다공성 형상기억합금에 대한 새로운 3차원 응력-변형률 모델을 제안하였다. 12%의 기공도를 갖는 Ni-Ti 형상기억합금에 대한 압축실험으로부터 구한 응력-변형률 선도와 본 연구에서 제안한 모델링에 의한 응력-변형률 관계를 비교한 결과 잘 일치함을 알 수 있었다. 기존의 다른 연구에서는 대부분 상변태 구간이 선형적으로 예측되었지만 본 연구에서는 비선형으로 예측되어 실험결과를 보다 잘 모사할 수 있었다.

• Composites Research
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• 제19권2호
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• pp.28-34
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• 2006

고온자전합성법과 스파크 플라즈마 소결법으로 여러 가지 $TiB_2$ 함유량을 갖는 $Cu-TiB_2$ 금속복합재료를 제조하였다. 점용접 전극과 미끄럼 접촉재로 사용하기 위해 인장특성, 경도, 마모저항 등의 물성치를 조사하였다. 강화재의 형상, 크기, 부피분율 등에 의해 복합재료의 특성이 달라지므로 유효물성치를 예측하기 위한 모델링이 필수적이다. 유한요소해석결과 유효탄성 계수가 실험치와 일치하는 것을 확인하였고 Eshelby 모델, Mori-Tanaka의 평균장 이론이 결합된 Eshelby 모델, 혼합법칙 등으로 복합재료의 탄성계수를 예측한 결과 Mori-Tanaka의 평균장 이론이 결합된 Eshelby 모델이 실험치를 사장 잘 묘사하는 것으로 나타났다.

• Composites Research
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• 제18권5호
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• pp.21-26
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• 2005

본 연구에서는 복합재의 등가 물성치를 예측하는 방법중 하나인 Mori-Tanaka의 평균장이론이 결합된 Eshelby 이론의 적용한계에 대해 유한요소해석을 통하여 강화재의 크기와 배치 측면에서 고찰하였다. 모델 복합재로 일정 체적비의 강화재를 포함하는 2차원 평판 복합재를 사용하였으며, 강화재의 크기를 변화시키고 또한 강화재를 규칙적 및 불규칙적으로 배치하였다. 이 복합재에 유한요소해석을 적용하여 수치적으로 복합재의 등가 물성치를 구하였으며, 수치해석결과를 Eshelby 이론으로 구한 등가 물성치와 비교하였다. Eshelby 이론으로 예측되는 복합재의 등가 물성치는 시편의 크기에 비해 강화재의 크기가 0.03이하가 되면 강화재의 배치와 관계없이 유한요소해석으로 구한 복합재의 평균 영계수와는 잘 일치하나, 평균 프와송비는 약 $20\%$의 차이를 보였다.

• Composites Research
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• 제17권5호
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• pp.54-60
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• 2004

복합재의 사전변형률과 형상기억합금의 형상기억효과를 유발하는 형상기억합금의 상변화량과의 관계를 예측하기 위하여 Eshelby의 등가개재물법과 Mori-Tanaka의 평균장이론을 이용한 새로운 3차원 모델을 제안하였다. 복합재 모델은 가공경화 현상을 갖는 알루미늄을 모재로, 단섬유 TiNi 형상기억합금을 강화재로 사용하였다. 모델 해석에 의하면 사전 변형률이 지극히 작은 영역에서는 사전변형률이 모두 강화재의 형상기억 효과를 유발하고, 이 보다 큰 영역에서 사전 변형률은 강화재의 형상기억 효과와 모재의 소성변형에 의한 것으로 나타났다. 이러한 복합재의 강화기구는 모재의 가공경화 현상과 형상기억 효과에 의한 항복응력 증가를 분리하여 제시되어야 한다.

• Computers and Concrete
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• 제19권3호
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• pp.333-338
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• 2017

In this paper, nonlinear vibration of embedded nanocomposite concrete is investigated based on Timoshenko beam model. The beam is reinforced by with agglomerated silicon dioxide (SiO2) nanoparticles. Mori-Tanaka model is used for considering agglomeration effects and calculating the equivalent characteristics of the structure. The surrounding foundation is simulated with Pasternak medium. Energy method and Hamilton's principal are used for deriving the motion equations. Differential quadrature method (DQM) is applied in order to obtain the frequency of structure. The effects of different parameters such as volume percent of SiO2 nanoparticles, nanoparticles agglomeration, elastic medium, boundary conditions and geometrical parameters of beam are shown on the frequency of system. Numerical results indicate that with increasing the SiO2 nanoparticles, the frequency of structure increases. In addition, considering agglomeration effects leads to decrease in frequency of system.

• Computers and Concrete
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• 제23권5호
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• pp.361-376
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• 2019

In this research, bending analysis of a micro sandwich skew plate with isotropic core and piezoelectric composite face sheets reinforced by carbon nanotube on the elastic foundations are studied. The classical plate theory (CPT) are used to model micro sandwich skew plate and to apply size dependent effects based on modified strain gradient theory. Eshelby-Mori-Tanaka approach is considered for the effective mechanical properties of the nanocomposite face sheets. The governing equations of equilibrium are derived using minimum principle of total potential energy and then solved by extended Kantorovich method (EKM). The effects of width to thickness ratio and length to width of the sandwich plate, core-to-face sheet thickness ratio, the material length scale parameters, volume fraction of CNT, the angle of skew plate, different boundary conditions and types of cores on the deflection of micro sandwich skew plate are investigated. One of the most important results is the reduction of the deflection by increasing the angle of the micro sandwich skew plate and decreasing the deflection by decreasing the thickness of the structural core. The results of this research can be used in modern construction in the form of reinforced slabs or stiffened plates and also used in construction of bridges, the wing of airplane.

• Computers and Concrete
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• 제22권1호
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• pp.117-122
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• 2018

The use of nanotechnology materials and applications in the construction industry should be considered for enhancing material properties. However, in this paper, the technical and economical assessment of applying silica nanoparticles for construction of concrete structure is studied. In order to obtain the equivalent material properties of the structure, the Mori-Tanaka model is used considering agglomeration of nanoparticles. The effect of using these nanoparticles on mechanical properties of concrete, such as the modulus of elasticity, compressive strength, as well as its indirect effect on armature percentage is investigated. Finally, the price of silica nanoparticles and its effect on the price increase of concrete structure is investigated. The results show that increasing the volume percent of silica nanoparticles up to 10% improves elastic modulus 111% and reduces amateur percentage up to 72%.

• Steel and Composite Structures
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• 제20권3호
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• pp.623-649
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• 2016

Most of the early studies on plates vibration are focused on two-dimensional theories, these theories reduce the dimensions of problems from three to two by introducing some assumptions in mathematical modeling leading to simpler expressions and derivation of solutions. However, these simplifications inherently bring errors and therefore may lead to unreliable results for relatively thick plates. The main objective of this research paper is to present 3-D elasticity solution for free vibration analysis of continuously graded carbon nanotube-reinforced (CGCNTR) rectangular plates resting on two-parameter elastic foundations. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. In this study, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes (CNTs). The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The formulations are based on the three-dimensional elasticity theory. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its very high accuracy and versatility. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and results reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. The novelty of the present work is to exploit Eshelby-Mori-Tanaka approach in order to reveal the impacts of the volume fractions of oriented CNTs, different CNTs distributions, various coefficients of foundation and different combinations of free, simply supported and clamped boundary conditions on the vibrational characteristics of CGCNTR rectangular plates. The new results can be used as benchmark solutions for future researches.

• Advances in concrete construction
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• 제1권3호
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• pp.239-252
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• 2013

Mortar microstructure is considered as a three-phase composite material, which is cement paste, fine aggregate and interfacial transition zone. Interfacial transition zone is the weakest link between the cement paste and fine aggregate, so it has a significant role to determine the properties of cementitious composites. In this study, specimens (w/c = 0.35, 0.45, 0.55) with various volume fractions of fine aggregate ($V_f$ = 0, 0.1, 0.2, 0.3 and 0.4) were cast and tested. To predict the equivalent migration coefficient ($M_e$) and migration coefficient of interfacial transition zone ($M_{itz}$), double-inclusion method and Mori-Tanaka theory were used to estimate. There are two stages to estimate and calculate the thickness of interfacial transition zone (h) and migration coefficient of interfacial transition zone ($M_{itz}$). The first stage, the data of experimental chloride ion migration coefficient ($M_s$) was used to calculate the equivalent migration coefficient of fine aggregate with interfacial transition zone ($M_e$) by Mori-Tanaka theory. The second stage, the thickness of interfacial transition zone (h) and migration coefficient of interfacial transition zone ($M_{itz}$) was calculated by Hori and Nemat-Nasser's double inclusion model. Between the theoretical and experimental data a comparison was conducted to investigate the behavior of interfacial transition zone in mortar and the effect of interfacial transition zone on the chloride migration coefficient, the results indicated that the numerical simulations is derived to the $M_{itz}/M_m$ ratio is 2.11~8.28. Additionally, thickness of interfacial transition zone is predicted from $10{\mu}m$, 60 to $80{\mu}m$, 70 to $100{\mu}m$ and 90 to $130{\mu}m$ for SM30, M35, M45 and M55, respectively.