• Smart Structures and Systems
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• 제29권3호
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• pp.387-393
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• 2022

This paper presents the vibration analysis of cracked ceramic-reinforced aluminum composite beams by using a method based on changes in modal strain energy. The crack is considered to be straight. The effective properties of composite materials of the beams are estimated through Mori-Tanaka micromechanical model. Comparison study and numerical simulations with various parameters; ceramic volume fraction, reinforcement aspect ratio, ratio of the reinforcement Young's modulus to the matrix Young's modulus and ratio of the reinforcement density to the matrix density are taken into investigation. Results demonstrate the pronounced effects of these parameters on intact and cracked ceramic aluminum beams.

• 마이크로전자및패키징학회지
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• 제9권4호
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• pp.35-45
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• 2002

열하중에 의한 언더필/칩 계면의 응력을 유한요소법을 이용하여 구하였다. 먼저 실리카 입자의 부피 분율이 언더필 재료의 물성에 미치는 영향을 알아보기 위하여 세 가지 재료 세트에 대하여 실리카 입자의 부피 분율에 따른 영계수, 포아슨비, 영팽창 계수를 Mori-Tanaka방법을 이용하여 계산하였고, 언더필과 칩이 형성하는 edge및 wedge에 대한 singularity를 계산하였다. 그 다음에는 앞에서 계산한 재료물성치를 가지고 실리카 입자의 부피 분율에 따른 언더필/칩 계면의 응력을 몇 가지 플립칩 형상에 대하여 살펴보았다. 언더필이 균일한 재료라는 가정과 플립칩 어셈블리를 구성하고 있는 재료들이 선형탄 성적거동을 하고 등방성을 보이며 그들의 성질이 온도에 무관하다는 가정 하에 다섯 가지의 플립칩 어셈블리 모델이 고려되었다.

• 비파괴검사학회지
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• 제18권2호
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• pp.112-120
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• 1998

입자 보강 복합재료의 부피분율을 평가하기 위한 와전류 비파괴 방법을 제시하였다. 제안된 방법은 복합재의 미시구조를 설명할 수 있는 이론 모델과 와전류에 의한 전기전도도 측정을 필요로 한다. 측정한 전도도를 이론 예측값과 같게 두면 미지의 입자 부피분율이 계산된다. Mori-Tanaka 방법에 기초한 전도도 해석 모델이 소개되어 있다. 이러한 접근 방법을 SiC 입자 보강 Al 기지 ($SiC_p/Al$) 복합재에 적용하였다. 이방법으로 보강재의 부피분율을 비교적 정확하게 결정할 수 있었다. 금속간 화합물이 부피분율 평가에 미치는 영향을 논하였으며, 또한 금속간 화합물의 전도도와 기하학적 성질이 보강 입자와 같은 경우, 이 두 상의 총 부피분율을 결정할 수 있는 방법을 제시하였다.

• Steel and Composite Structures
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• 제38권5호
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• pp.477-496
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• 2021

The main objective of this paper is to study vibration of sandwich open cylindrical panel with damaged core and FG face sheets based on three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. Three complicated equations of motion for the panel under consideration are semi-analytically solved by using 2-D differential quadrature method. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution and boundary conditions. It is seen that for the large amount of power-law index "P", increasing this parameter does not have significant effect on the non-dimensional natural frequency parameters of the FG sandwich curved panel. Results indicate that by increasing the value of isotropic damage parameter "D" up to the unity (fully damaged core) the frequency would tend to become zero. One can dictate the fiber variation profile through the radial direction of the sandwich panel via the amount of "P", "b" and "c" parameters. It should be noticed that with increase of volume fraction of fibers, the frequency parameter of the panels does not increase necessarily, so by considering suitable amounts of power-law index "P" and the parameters "b" and "c", one can get dynamic characteristics similar or better than the isotropic limit case for laminated FG curved panels.

• Journal of Advanced Marine Engineering and Technology
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• 제33권6호
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• pp.852-859
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• 2009

For the analysis of solids containing a number of microinclusions or microvoids, in which the mechanical effect of each inclusion or void, a numerical approach is need to be developed to understand the mechanical behavior of damaged solids containing these defects. In this study, the simulation method using the natural element method is proposed for the analysis of effective elastic moduli. The mechanical effect of each inclusion or void is considered by controlling the material constants for Gaussian points. The relationship between area fraction of microinclusions or microvoids and effective elastic moduli is studied to verify the validity of the proposed method. The obtained results are in good agreement with the theoretical results such as differential method, self-consistent method, Mori-Tanaka method, as well as the numerical results by rigid body spring model.

• Earthquakes and Structures
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• 제13권3호
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• pp.241-253
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• 2017

In this paper, dynamic response of the horizontal nanofiber reinforced polymer (NFRP) strengthened concrete beam subjected to seismic ground excitation is investigated. The concrete beam is modeled using hyperbolic shear deformation beam theory (HSDBT) and the mathematical formulation is applied to determine the governing equations of the structure. Distribution type and agglomeration effects of carbon nanofibers are considered by Mori-Tanaka model. Using the nonlinear strain-displacement relations, stress-strain relations and Hamilton's principle (virtual work method), the governing equations are derived. To obtain the dynamic response of the structure, harmonic differential quadrature method (HDQM) along with Newmark method is applied. The aim of this study is to investigate the effect of NFRP layer, geometrical parameters of beam, volume fraction and agglomeration of nanofibers and boundary conditions on the dynamic response of the structure. The results indicated that applied NFRP layer decreases the maximum dynamic displacement of the structure up to 91 percent. In addition, using nanofibers as reinforcement leads a 35 percent reduction in the maximum dynamic displacement of the structure.

• Structural Engineering and Mechanics
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• 제87권2호
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• pp.129-136
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• 2023

In this paper, dynamic buckling of truncated conical shell made of carbon nanotubes (CNTs) composite is studied. In aerospace industries, this category of structures is utilized extensively due to wide range of engineering applications. To calculate the effective material properties of the nanocomposite, The Mori-Tanaka model is applied. Also, the motion equations are derived with the assistance of the first order shear deformation theory (FSDT), Hamilton's principle and energy method. Besides, In order to solve motion equations and analyze dynamic instability region (DIR) of the structure, mixed model of differential quadrature method (DQM) and Bolotin's method is used. Moreover, investigation of the different parameters effects such as geometrical parameters and volume fraction of CNTs on the analysis of the DIR of the structure is done. In accordance with the obtained results, the DIR will occur at higher frequencies by increasing the volume fraction of CNTs.

• Steel and Composite Structures
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• 제49권3호
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• pp.349-359
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• 2023

Dynamic response and economic of a laminated porous concrete beam reinforced by nanoparticles subjected to harmonic transverse dynamic load is investigated considering structural damping. The effective nanocomposite properties are evaluated on the basis of Mori-Tanaka model. The concrete beam is modeled by the sinusoidal shear deformation theory (SSDT). Utilizing nonlinear strains-deflection, energy relations and Hamilton's principal, the governing final equations of the concrete laminated beam are calculated. Utilizing differential quadrature method (DQM) as well as Newmark method, the dynamic displacement of the concrete laminated beam is discussed. The influences of porosity parameter, nanoparticles volume percent, agglomeration of nanoparticles, boundary condition, geometrical parameters of the concrete beam and harmonic transverse dynamic load are studied on the dynamic displacement of the laminated structure. Results indicated that enhancing the nanoparticles volume percent leads to decrease in the dynamic displacement about 63%. In addition, with considering porosity of the concrete, the dynamic displacement enhances about 2.8 time.

• Computers and Concrete
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• 제19권6호
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• pp.745-753
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• 2017

Dynamic analysis of a concrete pipes armed with Silica ($SiO_2$) nanoparticles subjected to earthquake load is presented. The structure is modeled with first order shear deformation theory (FSDT) of cylindrical shells. Mori-Tanaka approach is applied for obtaining the equivalent material properties of the structure considering agglomeration effects. Based on energy method and Hamilton's principle, the motion equations are derived. Utilizing the harmonic differential quadrature method (HDQM) and Newmark method, the dynamic displacement of the structure is calculated for the Kobe earthquake. The effects of different parameters such as geometrical parameters of pipe, boundary conditions, $SiO_2$ volume percent and agglomeration are shown on the dynamic response of the structure. The results indicate that reinforcing the concrete pipes by $SiO_2$ nanoparticles leads to a reduction in the displacement of the structure during an earthquake.

• Computers and Concrete
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• 제20권3호
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• pp.361-368
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• 2017

Seismic response of the concrete column covered by nanofiber reinforced polymer (NFRP) layer is investigated. The concrete column is studied in this paper. The column is modeled using sinusoidal shear deformation beam theory (SSDT). Mori-Tanaka model is used for obtaining the effective material properties of the NFRP layer considering agglomeration effects. Using the nonlinear strain-displacement relations, stress-strain relations and Hamilton's principle, the motion equations are derived. Harmonic differential quadrature method (HDQM) along with Newmark method is utilized to obtain the dynamic response of the structure. The effects of different parameters such as NFRP layer, geometrical parameters of column, volume fraction and agglomeration of nanofibers and boundary conditions on the dynamic response of the structure are shown. The results indicated that applied NFRP layer decreases the maximum dynamic displacement of the structure. In addition, using nanofibersas reinforcement leads a reduction in the maximum dynamic displacement of the structure.