• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2000년도 가을 학술발표회 논문집(II)
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• pp.1145-1150
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• 2000

Concrete behaves as ductile material at high temperature. The existing stress-strain relationship is not valid at high temperature condition. Thus, stress-strain curve of concrete at high temperature is re-established by modifying Saenz's suggestion in this study. A constitutive model of concrete subjected to elevated temperature is also suggested. The model consists of three components; free thermal stain, mechanical strain and thermal creep strain. As the temperature increase, the thermal creep becomes more critical to the failure of concrete. The thermal creep strain of concrete is derived from the modified power-law relation for the steady state creep. The proposed equation for thermal creep employs a Dorn's temperature compensated time theorem

• Computers and Concrete
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• 제2권4호
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• pp.249-266
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• 2005

In the present paper a transient three-dimensional thermo-mechanical model for concrete is presented. For given boundary conditions, temperature distribution is calculated by employing a three-dimensional transient thermal finite element analysis. Thermal properties of concrete are assumed to be constant and independent of the stress-strain distribution. In the thermo-mechanical model for concrete the total strain tensor is decomposed into pure mechanical strain, free thermal strain and load induced thermal strain. The mechanical strain is calculated by using temperature dependent microplane model for concrete (O$\check{z}$bolt, et al. 2001). The dependency of the macroscopic concrete properties (Young's modulus, tensile and compressive strengths and fracture energy) on temperature is based on the available experimental database. The stress independent free thermal strain is calculated according to the proposal of Nielsen, et al. (2001). The load induced thermal strain is obtained by employing the biparabolic model, which was recently proposed by Nielsen, et al. (2004). It is assumed that the total load induced thermal strain is irrecoverable, i.e., creep component is neglected. The model is implemented into a three-dimensional FE code. The performance of headed stud anchors exposed to fire was studied. Three-dimensional transient thermal FE analysis was carried out for three embedment depths and for four thermal loading histories. The results of the analysis show that the resistance of anchors can be significantly reduced if they are exposed to fire. The largest reduction of the load capacity was obtained for anchors with relatively small embedment depths. The numerical results agree well with the available experimental evidence.

• Structural Engineering and Mechanics
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• 제90권1호
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• pp.1-18
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• 2024

The present study conducts a thorough analysis of thermal vibrations in functionally graded porous nanocomposite beams within a thermal setting. Investigating the temperature-dependent material properties of these beams, which continuously vary across their thickness in accordance with a power-law function, a finite element approach is developed. This approach utilizes a nonlocal strain gradient theory and accounts for a linear temperature rise. The analysis employs four different patterns of porosity distribution to characterize the functionally graded porous materials. A novel two-variable shear deformation beam nonlocal strain gradient theory, based on trigonometric functions, is introduced to examine the combined effects of nonlocal stress and strain gradient on these beams. The derived governing equations are solved through a 3-nodes beam element. A comprehensive parametric study delves into the influence of structural parameters, such as thicknessratio, beam length, nonlocal scale parameter, and strain gradient parameter. Furthermore, the study explores the impact of thermal effects, porosity distribution forms, and material distribution profiles on the free vibration of temperature-dependent FG nanobeams. The results reveal the substantial influence of these effects on the vibration behavior of functionally graded nanobeams under thermal conditions. This research presents a finite element approach to examine the thermo-mechanical behavior of nonlocal temperature-dependent FG nanobeams, filling the gap where analytical results are unavailable.

• Smart Structures and Systems
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• 제5권6호
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• pp.591-612
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• 2009

New insights are presented in simplified modeling and analysis of free vibrations of piezoelectric - based smart structures and systems. These consist, first, in extending the wide used piezoelectric-thermal analogy (TA) simplified modeling approach in currently static actuation to piezoelectric free-vibrations under short-circuit (SC) and approximate open-circuit (OC) electric conditions; second, the popular piezoelectric strain induced - potential (IP) simplified modeling concept is revisited. It is shown that the IP resulting frequencies are insensitive to the electric SC/OC conditions; in particular, SC frequencies are found to be the same as those resulting from the newly proposed OC TA. Two-dimensional plane strain (PStrain) and plane stress (PStress) free-vibrations problems are then analyzed for above used SC and approximate OC electric conditions. It is shown theoretically and validated numerically that, for both SC and OC electric conditions, PStress frequencies are lower than PStrain ones, and that 3D frequencies are bounded from below by the former and from above by the latter. The same holds for the modal electro-mechanical coupling coefficient that is retained as a comparator of presented models and analyses.

• Advances in nano research
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• 제14권5호
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• pp.475-493
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• 2023

In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.

• Applied Microscopy
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• 제25권2호
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• pp.73-79
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• 1995

The oxidation of silicon wafers is an essential step in the fabrication of semiconductor devices. It is known to induce degradation of electrical properties and lattice strain of Si substrate from thermal oxidation process due to charged interface and thermal expansion mismatch from thermally grown SiO, film. In this study, convergent beam electron diffraction technique is employed to directly measure the lattice strains in Si(100) and $4^{\circ}$ - off Si(100) substrates with thermally grown oxide layer at $1200^{\circ}C$ for three hours. The ratios of {773}-{973}/{773}-{953} Higher Order Laue Zone lines were used at [012] zone axis orientation. Lattice parameters of the Si substrate as a function of distance from the interface were determined from the computer simulation of diffraction patterns. Correction value for the accelerating voltage was 0.2kV for the kinematic simulation of the [012]. HOLZ patterns. The change in the lattice strain profile before and after removal of oxide films revealed the magnitudes of intrinsic strain and thermal strain components. It was shown that $4^{\circ}$ -off Si(100) had much lower intrinsic strain as surface steps provide effective sinks for the free Si atoms produced during thermal oxidation. Thermal strain in the Si substrate was in compression very close to the interface and high concentration of Si interstitials appeared to modify the thermal expansion coefficient of Si.

• Steel and Composite Structures
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• 제44권4호
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• pp.557-567
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• 2022

Nonlinear free vibration analysis of a functionally graded beam resting on the nonlinear viscoelastic foundation is studied with uniform temperature rising. The non-linear strain-displacement relationship is considered in the finite strain theory. The governing nonlinear dynamic equation is derived based on the finite strain theory with using of Hamilton's principle. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The influences of temperature rising, material distribution parameter, nonlinear viscoelastic foundation parameters on the nonlinear free response and phase trajectory are investigated. In this paper, it is aimed that a contribution to the literature for nonlinear thermal vibration solutions of a functionally graded beam resting on the nonlinear viscoelastic foundation by using of multiple time scale method.

• 콘크리트학회논문집
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• 제13권3호
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• pp.268-276
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• 2001

본 논문은 고온에서의 콘크리트 재료모델을 연구하였다. 콘크리트 응력-변형률 곡선은 온도가 증가함에 따라 그 형태가 변한다. 온도에 따른 콘크리트 재료거동의 변화를 나타내기 위하여 변형된 Saenz 제안식을 이용하여 응력-변형률 관계를 표시하였다. 고온에서의 급격한 변형률의 증가현상을 설명하기 위하여, 콘크리트의 변형률 성분을 순수 열팽창 변형률, 열적크리프 변형률, 과도 변형률 및 역학적 변형률로 구분하여 나타내었다. 열적크리프 변형률은 Baily-Norton의 장기크리프 곡선 식을 수정.제안하여 1축 실험 결과를 온도, 시간 및 응력의 함수로 표현하였고, 또한 유효응력 및 유효변형률 개념을 도입하여 다차원에서도 적용할 수 있는 모델을 제시하였다. 과도 변형률을 제안하여 다공탄성 거동을 가정한 콘크리트 내에 포함된 공극 및 수분의 작용을 역학적 거동의 영향을 분석하고자 하였다. 마지막으로, 본 논문에서 제시한 고온에서의 콘크리트 재료모델을 이용한 해석결과를 실제 화재실험자료와 비교하였다.

• Structural Engineering and Mechanics
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• 제64권6권
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• pp.683-693
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• 2017

According to a generalized nonlocal strain gradient theory (NSGT), dynamic modeling and free vibrational analysis of nanoporous inhomogeneous nanoplates is presented. The present model incorporates two scale coefficients to examine vibration behavior of nanoplates much accurately. Porosity-dependent material properties of the nanoplate are defined via a modified power-law function. The nanoplate is resting on a viscoelastic substrate and is subjected to hygro-thermal environment and in-plane linearly varying mechanical loads. The governing equations and related classical and non-classical boundary conditions are derived based on Hamilton's principle. These equations are solved for hinged nanoplates via Galerkin's method. Obtained results show the importance of hygro-thermal loading, viscoelastic medium, in-plane bending load, gradient index, nonlocal parameter, strain gradient parameter and porosities on vibrational characteristics of size-dependent FG nanoplates.

• 마이크로전자및패키징학회지
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• 제20권3호
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• pp.37-44
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• 2013

유연 솔더가 실장된 패키지와 무연 솔더가 실장된 패키지의 온도에 따른 변형 거동은 솔더 자체의 물성치 뿐만 아니라 패키지를 구성하는 재료의 물성치에도 큰 영향을 받는다고 알려져 있다. 본 논문에서는 스트레인 게이지의 온도특성을 이용하여 미지 재료의 열팽창계수를 결정하는 방법을 정립하고, 반도체 패키지 몰딩 화합물의 열팽창계수를 실험적으로 구하였다. 탄소강과 알루미늄 시편을 기준 시편으로 사용하고 스트레인 게이지 측정을 통하여 온도에 따른 유연 솔더용 몰딩 화합물과 무연 솔더용 몰딩 화합물의 열팽창계수를 구하고, 무아레 간섭계를 이용하여 비접촉적으로 열팽창 계수를 측정하여 결과를 비교하였다. 기준 시편에 따른 두 가지 스트레인 게이지 실험 결과와 무아레 실험 결과가 잘 일치하여서 실험방법에 신뢰성이 있는 것을 보였다. 유연 솔더용 몰딩 화합물의 경우에는 열팽창계수가 온도에 관계없이 약 $15.8ppm/^{\circ}C$로 측정되었고, 무연 솔더용의 경우에는 $100^{\circ}C$이하의 온도에서 몰딩 화합물의 열팽창계수는 약 $9.9ppm/^{\circ}C$이었으나 $100^{\circ}C$이상에서는 온도가 증가함에 따라 열팽창계수가 급격하게 증가되어 $130^{\circ}C$에서는 $15.0ppm/^{\circ}C$의 값을 가졌다.