• Structural Engineering and Mechanics
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• 제54권5호
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• pp.855-875
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• 2015

Many novel materials exhibit a property of different elastic moduli in tension and compression. One such material is graphene, a wonder material, which has the highest strength yet measured. Investigations on buckling problems for structures with different moduli are scarce. To address this new problem, firstly, the nondimensional expression of the relation between offset of neutral axis and deflection curve is derived based on the phased integration method, and then using the energy method, load-deflection relation of the rod is determined; Secondly, based on the improved constitutive model for different moduli, large deformation finite element formulations are developed and combined with the arc-length method, finite element iterative program for rods with different moduli is established to obtain buckling critical loads; Thirdly, material mechanical properties tests of graphite, which is the raw material of graphene, are performed to measure the tensile and compressive elastic moduli, moreover, buckling tests are also conducted to investigate the buckling behavior of this kind of graphite rod. By comparing the calculation results of the energy method and finite element method with those of laboratory tests, the analytical model and finite element numerical model are demonstrated to be accurate and reliable. The results show that it may lead to unsafe results if the classic theory was still adopted to determine the buckling loads of those rods composed of a material having different moduli. The proposed models could provide a novel approach for further investigation of non-linear mechanical behavior for other structures with different moduli.

• Geomechanics and Engineering
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• 제19권4호
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• pp.353-360
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• 2019

The elastic modulus is an important parameter to characterize the property of rock. It is common knowledge that the strengths of rocks are significantly different under tension and compression. However, little attention has been paid to the bi-modularity of rock. To validate whether the rock elastic moduli in tension and compression are the same, Brazilian disc, direct tension and compression tests were conducted. A horizontal laser displacement meter and a pair of vertical and transverse strain gauges were applied. Four types of materials were tested, including three types of rock materials and one type of steel material. A comprehensive comparison of the elastic moduli based on different experimental results was presented, and a tension-compression anisotropy model was proposed to explain the experimental results. The results from this study indicate that the rock elastic modulus is different under tension and compression. The ratio of the rock elastic moduli under compression and tension ranges from 2 to 4. The rock tensile moduli from the strain data and displacement data are approximate. The elastic moduli from the Brazilian disc test are consistent with those from the uniaxial tension and compression tests. The Brazilian disc test is a convenient method for estimating the tensile and compressive moduli of rock materials.

• 대한수학회지
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• 제58권2호
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• pp.501-523
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• 2021

We study the geometry of the moduli space of elliptic stable maps to projective space. The main component of the moduli space of elliptic stable maps is singular. There are two different ways to desingularize this space. One is Vakil-Zinger's desingularization and the other is via the moduli space of logarithmic stable maps. Our main result is a proof of the direct geometric relationship between these two spaces. For degree less than or equal to 3, we prove that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger's desingularization.

• Structural Engineering and Mechanics
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• 제36권3호
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• pp.363-380
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• 2010

Materials which exhibit different elastic moduli in tension and compression are known as bimodular materials. The bimodular materials model, which is founded on the criterion of positive-negative signs of principal stress, is important for the structural analysis and design. However, due to the inherent complexity of the constitutive relation, it is difficult to obtain an analytical solution of a bimodular bending components except in particular simple problems. Based on the existent simplified model, this paper solves analytically bending thin plates with different moduli in tension and compression. By using the continuity conditions of stress components in unknown neutral layer, we determine the location of the neutral layer, and derive the governing differential equation for deflection, the flexural rigidity, and the internal forces in the thin plate. We also use a circular thin plate with bimodulus to illustrate the application of this solution derived in this paper. The results show that the introduction of different moduli has influences on the flexural stiffness of the bending thin plate.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1995년도 봄 학술발표회 논문집
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• pp.345-349
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• 1995

Although heterogeneous materials consisted of micro-constituents are complicated, it is possible to evaulate effective elastic moduli by using micro-mechanics models. In order to evaluate effective elastic moduli of concrete, all aggregates in a representative volume element(RVE) are assumed spherical and randomly distributed. A dilute distribution of inclusions is considered first, and the corresponding overall elastic moduli of the RVE are estimated. Then, the self-consistent method is used in order to take into account the interaction effects. The elastic moduli of concrete are calculated using the models and compared with those of experiment for different volume fractions of the aggregates and elastic moduli of the mortar and the aggregates.

• 대한수학회지
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• 제54권6호
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• pp.1759-1786
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• 2017

We examine the moduli space of oriented locally homogeneous manifolds of Type ${\mathcal{A}}$ which have non-degenerate symmetric Ricci tensor both in the setting of manifolds with torsion and also in the torsion free setting where the dimension is at least 3. These exhibit phenomena that is very different than in the case of surfaces. In dimension 3, we determine all the possible symmetry groups in the torsion free setting.

• 한국방재학회 논문집
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• 제6권1호
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• pp.39-48
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• 2006

본 시험은 다양한 sine파형을 가진 인장 및 압축 하중 하에서 아스팔트 혼합물의 모듀율값 을 비교평가하기 위하여 수행되었다. 즉, 휴식시간을 가진 반복 인장 haversine 하중, 휴식시간을 가진 반복 압축 haversine 하중, 주기적 인장하중, 주기적 압축하중, 그리고 주기적 인장-압축 반복하중이라는 총 5개의 하중형태가 32, 50, 68, 86, $104^{\circ}F$ (0, 10, 20, 30, $40^{\circ}C$) 라는 5개의 온도하에서 평가되었다. 시험결과, 휴식시간을 가진 반복 haversine 하중으로 인한 아스팔트 콘크리트의 인장 및 압축 모듀율 값은 저온에서 유사한 값을 나타내었지만, 고온에서는 상이한 값을 보였다. 특히, 고온에서 압축 모듀율 값은 인장 모듀율 값보다 높은 수치를 보였다. 또한, 저온에서 일축 직접인장 시험으로부터 구한 모듀율 값은 간접 인장시험으로부터 구한 모듀율 값보다 높은 값을 나타내었다. 그러나, 고온에서는 서로 유사한 값을 보였다. 일반적으로, 휴식시간을 갖는 반복 haversine 하중을 이용하여 얻은 모듀율 값은 주기적 sine파형을 가진 하중으로부터 구한 모듀율 값보다 항상 낮은 값을 나타내었으며 그 두 가지 하중으로부터 구한 모듀율 값의 차이는 온도가 감소함에 따라 더욱 증가되었다.

• 비파괴검사학회지
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• 제36권1호
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• pp.1-8
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• 2016

Single crystalline silicon wafers having (100), (110), and (111) directions are employed as specimens for obtaining slowness profiles. Leaky Lamb waves (LLW) from immersed wafers were detected by varying the incident angles of the specimens and rotating the specimens. From an analysis of LLW signals for different propagation directions and phase velocities of each specimen, slowness profiles were obtained, which showed a unique symmetry with different symmetric axes. Slowness profiles were compared with elastic moduli of each wafer. They showed the same symmetries as crystal structures. In addition, slowness profiles showed expected patterns and values that can be inferred from elastic moduli. This implies that slowness profiles can be used to examine crystal structures of anisotropic solids.

• Geomechanics and Engineering
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• 제24권4호
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• pp.349-358
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• 2021

The Brazilian test has been widely used to determine the indirect tensile strength of rock, concrete and other brittle materials. The basic assumption for the calculation formula of Brazilian tensile strength is that the elastic moduli of rock are the same both in tension and compression. However, the fact is that the elastic moduli in tension and compression of most rocks are different. Thus, the formula of Brazilian tensile strength under the assumption of isotropy is unreasonable. In the present study, we conducted Brazilian tests on flat disk-shaped rock specimens and attached strain gauges at the center of the disc to measure the strains of rock. A tension-compression bi-modular model is proposed to interpret the data of the Brazilian test. The relations between the principal strains, principal stresses and the ratio of the compressive modulus to tensile modulus at the disc center are established. Thus, the tensile and compressive moduli as well as the correct tensile strength can be estimated simultaneously by the new formulas. It is found that the tensile and compressive moduli obtained using these formulas were in well agreement with the values obtained from the direct tension and compression tests. The formulas deduced from the Brazilian test based on the assumption of isotropy overestimated the tensile strength and tensile modulus and underestimated the compressive modulus. This work provides a new methodology to estimate tensile strength and moduli of rock simultaneously considering tension-compression bi-modularity.

• 한국세라믹학회지
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• 제26권6호
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• pp.850-854
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• 1989

The elastic moduli and dissolution rates of 15 glasses with different mole ratios of sodium-magnasium-phosphate as potential non-toxic biomaterials were investigated. In this study, a 3-pint bending test, sonic resonance technique, and theoretical calculation were used to evaluate the modulus of elasticity. The dissolution rates at 37$^{\circ}C$(human body temperature) were determined by the measurement of mass changes in each sample for 24 weeks.