• Tribology and Lubricants
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• 제28권4호
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• pp.173-177
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• 2012

We used contact resonance force microscopy (CRFM) technique to determine the quantitative elastic properties of multiple materials integrated on the sub micrometer scale. The CRFM approach measures the frequencies of an AFM cantilever's first two flexural resonances while in contact with a material. The plain strain modulus of an unknown or test material can be obtained by comparing the resonant spectrum of the test material to that of a reference material. In this study we examined the following bumping materials for flip chip by using copper electrode as a reference material: NiP, Solder (Sn-Au-Cu alloy) and under filled epoxy. Data were analyzed by conventional beam dynamics and contact dynamics. The results showed a good agreement (~15% difference) with corresponding values determined by nanoindentaion. These results provide insight into the use of CRFM methods to attain reliable and accurate measurements of elastic properties of materials on the nanoscale.

• Structural Engineering and Mechanics
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• 제85권6호
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• pp.717-728
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• 2023

The effect of temperature dependent material properties on the free vibration of FG porous beams is investigated in the present paper. A quasi-3D shear deformation solution is used involves only three unknown function. The mechanical properties which are considered to be temperature-dependent as well as the porosity distributions are assumed to gradually change along the thickness direction according to defined law. The beam is supposed to be simply supported and lying on variable elastic foundation. The differential equation system governing the free vibration behavior of porous beams is derived based on the Hamilton principle. Navier's method for simply supported systems is then used to determine and compute the frequencies of FG porous beam. The results of the present formulation are validated by comparing with those available literatures. Finally, the effects of several parameters such as porosity distribution and the parameters of variable elastic foundation on the free vibration behavior of temperature-dependent FG beams are presented and discussed in detail.

• 대한기계학회논문집A
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• 제28권6호
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• pp.816-825
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• 2004

In this work, effects of hyper-elastic rubber material properties on the indentation load-deflection curve and subindenter deformation are examined via finite element (FE) analyses. An optimal location for data analysis is selected, which features maximum strain energy density and negligible frictional effect. We then contrive two normalized functions, which map an indentation load vs. deflection curve into a strain energy density vs. first invariant curve. From the strain energy density vs. first invariant curve, we can extract the rubber material properties. This new spherical indentation approach produces the rubber material properties in a manner more effective than the common uniaxial tensile/com-pression tests. The indentation approach successfully measures the rubber material properties and the corresponding nominal stress-strain curve with an average error less than 3%.

• Elastomers and Composites
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• 제39권1호
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• pp.23-35
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• 2004

본 연구에서는 먼저 유한요소해석을 통해 주요 물성계수들이 압입시 하중-변위 곡선형상에 미치는 영향을 분석하였다. 또한 유한요소 압입해석을 통해 마찰계수의 영향으로 하중-변위 곡선, 시편하부의 단위부피당 변형에너지 및 변형률 주불변량이 바뀌지 않는 최적 압입깊이와 시편하부지점을 선정하였다. 이러한 관찰을 통해 하나의 요소에서 얻어지는 단위부피당 변형 에너지와 변형률 주불변량을 하중-변위 데이터와 모사 시킬 수 있는 무차원 함수를 얻을 수 있었으며, 이 과정에서 예측된 물성계수를 바탕으로 공칭응력-공칭변형률 곡선을 얻을 수 있었다.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2002년도 추계학술발표대회 논문집
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• pp.100-105
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• 2002

This paper predicts the material properties of spatially reinforced composites (SRC) and analyzes the thermo-elastic behavior of a kick motor nozzle manufactured from that material. To find the appropriate SRC structure for the nozzle throat that satisfies given design conditions, the equivalent material properties of the SRC are predicted using the superposition method for those of rod and matrix. Studied are the elastic behavior, temperature distribution, and thermo-elastic behavior of a kick motor nozzle composed of carbon/carbon SRC as a throat part. The elastic deformation of the nozzle composed of 3D carbon/carbon SRC shows asymmetry in a circumferential direction. However, 4D carbon/carbon SRC nozzle shows uniform deformation in the circumferential direction. Stress concentration in connecting parts of the kick motor nozzle is ultimately high due to the high temperature gradient in each connecting part. The thermo-elastic deformations of both the 3D and the 4D SRC nozzles are uniform in the circumferential direction due to the isotropy of CTE of each SRC. The deformation of the 3D SRC nozzle is a slightly smaller than that of the 4D SRC nozzle in the nozzle throat, which is favorably effective on rocket thrust. The circumferential stress is the most critical component of the kick motor nozzle. The 4D SRC nozzle having 1,1,1,1.7 diameters in each direction has the smallest circumferential stress among several SRC nozzles.

• Steel and Composite Structures
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• 제16권1호
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• pp.77-96
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• 2014

In this paper, magneto-thermo-elastic problem of a thick truncated conical shell immersed in a uniform magnetic field and subjected to internal pressure is investigated. Material properties of the shell including the elastic modulus, magnetic permeability, coefficients of thermal expansion and conduction are assumed to be isotropic and graded through the thickness obeying the simple power law distribution, while the poison's ratio is assumed to be constant. The temperature distribution is assumed to be a function of the thickness direction. Governing equations of the truncated conical shell are derived in terms of components of displacement and thermal fields and discretised with the help of differential quadrature (DQ) method. Results are obtained for different values of power law index of material properties and effects of thermal load on displacement, stress, temperature and magnetic fields are studied. Results of the present method are compared with those of the finite element method.

• Structural Engineering and Mechanics
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• 제50권3호
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• pp.403-417
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• 2014

The present paper addresses a general formulation for the thermo elastic analysis of a functionally graded cylindrical shell subjected to external loads. The shear deformation theory and energy method is employed for this purpose. This method presents the final relations by using a set of second order differential equations in terms of integral of material properties along the thickness direction. The proposed formulation can be considered for every distribution of material properties, whether functional or non functional. The obtained formulation can be used for manufactured materials or structures with numerical distribution of material properties which are obtained by using the experiments. The governing differential equation is applied for two well-known functionalities and some previous results are corrected with present true results.

• Structural Engineering and Mechanics
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• 제18권1호
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• pp.91-112
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• 2004

Concrete is a composite material and at meso-level, may be assumed to be composed of three phases: aggregate, mortar-matrix and aggregate-matrix interface. It is postulated herein that although non-linear material parameters are generally used to model this composite structure by finite element method, linear elastic fracture mechanics principles can be used for modelling at the meso level, if the properties of all three phases are known. For this reason, a novel meso-mechanical approach for concrete fracture which uses the composite material model with distributed-phase for elastic properties of phases and considers the size effect according to linear elastic fracture mechanics for strength properties of phases is presented in this paper. Consequently, the developed model needs two parameters such as compressive strength and maximum grain size of concrete. The model is applied to three most popular fracture mechanics approaches for concrete namely the two-parameter model, the effective crack model and the size effect model. It is concluded that the developed model well agrees with considered approaches.

• Advances in aircraft and spacecraft science
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• 제6권3호
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• pp.207-223
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• 2019

Current investigation deals with the thermal stability characteristics of carbon nanotube reinforced composite beams (CNTRC) on elastic foundation and subjected to external uniform temperature rise loading. The single-walled carbon nanotubes (SWCNTs) are supposed to have a distribution as being uniform or functionally graded form. The material properties of the matrix as well as reinforcements are presumed to be temperature dependent and evaluated through the extended rule of mixture which incorporates efficiency parameters to capture the size dependency of the nanocomposite properties. The governing differential equations are achieved based on the minimum total potential energy principle and Euler-Bernoulli beam model. The obtained results are checked with the available data in the literature. Numerical results are supplied to examine the effects of numerous parameters including length to thickness ratio, elastic foundations, temperature change, and nanotube volume fraction on the thermal stability behaviors of FG-CNT beams.

• 전산구조공학
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• 제10권2호
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• pp.225-232
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• 1997

서로 다른 기지의 성질을 갖는 재료들을 혼합하여 만든 합성재료의 새로운 물성치는 일반적으로 실험으로 규명하고 있다. 혼합하는 재료들의 체적비에 따라 실험으로 측정한 합성재료의 탄성계수와 포와송비는 그 합성재료로 만들어지는 구조물의 역학적 거동을 예측하는 해석적 모델의 기본자료로 사용된다. 합성재료 탄성물성치의 수치적 예측은 합성재료에 대한 유한요소 모델로 해석한 정적변위와 균질.등방성으로 가정한 모델을 해석한 정적변위와의 차이를 최소화하는 구속적 비선형 최적화기법을 사용하여 수행하였다. 유한요소 모델은 체적비에 따라 혼합물질을 분배하기 용이하도록 제안하였으며 구속조건 및 하중조건은 일축인장에 의한 거동을 예측하도록 설정하였다. 본 논문에서는 고체입자를 섞어 만든 합성재료의 탄성물성치를 예제를 통하여 수치적으로 예측하고 그 결과를 실험결과 및 이론식들과 비교.검토하였다.