• Structural Engineering and Mechanics
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• 제74권1호
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• pp.83-90
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• 2020

Several classical and higher order plate theories were used to study the buckling of functionally graded material (FGM) plates. In the great majority of research, a power function is used to represent metal and ceramic material transverse distribution (P-FGM). Therefore, the effect of having other transverse variation of material properties on the buckling behavior of thick rectangular FGM plates was not properly addressed. In the present work, this effect is investigated using the Third order Shear Deformable Theory (TSDT) for the case of simply supported FGM plate. Both a sigmoid function and an exponential functions are used to represent the transverse gradual property variation. The plate governing equations are combined with a Navier type expanded solution of the unknown displacements to derive the buckling equation in terms of the pre-buckling in-plane loads. Finally, the critical in-plane load is calculated for the different buckling modes. The model is verified by a comparison of the calculated buckling loads with available published results of Al-SiC P-FGM plates. The conducted parametric study shows that manufacturing FGM plates with sigmoid variation of properties in the thickness direction increases the buckling load considerably. This improvement is found to be more significant for the case of thick plates than that of thin plates. Results also show that this stiffening-like effect of the sigmoid function profile is more evident for cases where the in-plane loads are applied along the shorter edge of the plate.

• 전자공학회논문지A
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• 제33A권11호
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• pp.120-127
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• 1996

In the WKB analysis, we propose the new forms of the trial eigenfunctions which not only converge at the turning points but also approximate to the conventional WKB solutions away from the turning points. The eigenvalue equation of multiple waveguides with graded index profile are derived by using the proposed WKB analysis and the transfer matrix method. The drived equation sare represented in the recursive form. The results of the eigenvalue equation sare comapred with those of the FDM, one of the well-known computational methods, for a three-waveguide coupler.

• Advances in Computational Design
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• 제5권4호
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• pp.397-416
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• 2020

Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

• Structural Engineering and Mechanics
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• 제51권4호
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• pp.627-641
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• 2014

Functionally graded steels (FGSs) are a family of functionally graded materials (FGMs) consisting of ferrite (${\alpha}$), austenite (${\gamma}$), bainite (${\beta}$) and martensite (M) phases placed on each other in different configurations and produced via electroslag remelting (ESR). In this research, the flow stress of dual layer austenitic-martensitic functionally graded steels under hot deformation loading has been modeled considering the constitutive equations which describe the continuous effect of temperature and strain rate on the flow stress. The mechanism-based strain gradient plasticity theory is used here to determine the position of each layer considering the relationship between the hardness of the layer and the composite dislocation density profile. Then, the released energy of each layer under a specified loading condition (temperature and strain rate) is related to the dislocation density utilizing the mechanism-based strain gradient plasticity theory. The flow stress of the considered FGS is obtained by using the appropriate coefficients in the constitutive equations of each layer. Finally, the theoretical model is compared with the experimental results measured in the temperature range $1000-1200^{\circ}C$ and strain rate 0.01-1 s-1 and a sound agreement is found.

• 한국광학회지
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• 제17권6호
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• pp.493-499
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• 2006

Modified Airy 함수를 이용하여 언덕형 굴절률 분포를 갖는 HOF를 해석하였으며, 정교한 결과를 갖는 고유 방정식을 도출하였다. 언덕형 HOF의 경우 기존의 계단형 HOF에 비하여 중공 영역 내 감쇠 전계의 기울기를 임의로 가파르게 조절할 수 있음을 보였다.

• Journal of the Optical Society of Korea
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• 제19권2호
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• pp.188-198
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• 2015

The validity of applying the Modified Airy Function (MAF) method to the problems of graded-index optical waveguides and graded potential barrier analysis was critically examined. In the former case, the method yielded very accurate results from the derived eigenvalue equations. In the latter case, however, the same method produced results that deviated significantly from exact numerical results for barriers with a smooth peak. The causes of the discrepancies were investigated in detail.

• Structural Engineering and Mechanics
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• 제71권1호
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• pp.23-35
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• 2019

In this study we derive the governing equations of a functionally graded piezoelectric disk, subjected to thermo-electro-mechanical loads. First order shear deformation theory is used for description of displacement field. Principles of minimum potential energy is used to derive governing equations in terms of components of the displacement field and the electric potential. The governing equations are derived for a disk with variable thickness. The numerical results are presented in terms of important parameters of the problem such as profile of variable thickness, in-homogeneous index and other related parameters.

• 대한전자공학회논문지SD
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• 제37권2호
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• pp.28-37
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• 2000

수정된 Airy 함수들과 WKB 시도해를 조합하여 언덕형 굴절율 분포를 가지는 광섬유에 대한 매우 정확한 고유방정식을 수학적으로 유도하였다. 적절한 경계조건을 적용하여 일반적인 WKB 방법이 가지는 고유한 오차 문제를 개선하도록 위상 천이 보정항 δ를 이끌어냈다. 모의 전산을 통하여, 유도된 고유방정식의 결과가 유한차분법에 의한 결과와 잘 일치함을 보였다.

• 대한전기학회논문지
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• 제45권1호
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• pp.146-158
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• 1996

The WKB method has been widely used in evaluating of the propagation characteristics of planar waveguides with graded-index profiles. This method, however, yields large errors when a turning point is near or at the discontinuity in the presence of the index discontinuity or index slope discontinuity. Especially, in the case of a truncated-index profile, this phenomenon appears more clearly in the low-order modes and near the cutoff regions. The MWKB method is introduced to reduce these inherent errors of the conventional WKB method. The MWKB method is based on both the linearization of the index profile from an index discontinuity and the introduction of a virtual turning point. It is noticed that the b-v curves obtained by the MWKB method agree well with those of the finite-difference method, and that the phase shift at a turning point depends on both the index profile and its propagation constant. (author). refs., figs.

• Journal of Oral Medicine and Pain
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• 제30권3호
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• pp.353-360
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• 2005

측두하악장애 연구진단기준 (Research Diagnostic Criteria for Temporomandibular Disorders; RDC/TMD)을 이용하여 측두하악장애 환자들에서 심리학적 상태 및 턱기능장애의 정도가 통증의 정도 및 지속기간, 통증과 관련된 일상생활 장애의 정도 및 기간, 만성통증척도에 미치는 영향 등을 알아보기 위하여 RDC/TMD axis I criteria에 따라 측두하악장애로 진단받은 평균연령 30.1$\pm$12.5 세인 93 명의 환자들(남성 17명, 여성 76명)을 대상으로 RDC/TMD axis II 병력 설문지를 작성하게 한 뒤, 우울증점수, 신체화장애점수, 턱기능장애점수와 만성통증척도의 통증 강도, 통증 지속기간, 통증과 연관된 장애 점수, 통증과 연관된 장애의 기간 및 만성통증척도 사이의 연관성을 분석하여 다음과 같은 결론을 얻었다. 1. 93명의 측두하악장애 환자들에서 만성통증척도의 경도의 장애를 보이는 군 (low disability group, grade I and II)은 42.0% 이었으며, 심도의 장애를 보이는 군 (high disability group, grade III and IV)은 51.5% 이었다. 2. 우울증점수는 통증 강도, 통증 지속기간, 통증과 연관된 장애 점수, 통증과 연관된 장애의 기간, 만성통증척도 모두에 통계적으로 유의한 영향을 미치지 않았다. 3. 신체화장애점수는 통증 강도 (p<0.01), 통증과 연관된 장애의 기간 (p<0.01), 만성통증척도 (p<0.01)에 유의한 영향을 미쳤으나, 통증 지속기간이나 통증과 연관된 장애 점수에는 통계적으로 유의한 영향을 미치지 않았다. 4. 턱기능장애점수는 통증 강도 (p<0.001), 통증과 연관된 장애의 기간 (p<0.01), 만성통증척도 (p<0.001)에 유의한 영향을 미쳤으나, 통증 지속기간이나 통증과 연관된 장애 점수에는 통계적으로 유의한 영향을 미치지 않았다. 측두하악장애환자에서 신체화장애와 턱기능장애는 환자가 느끼는 통증의 강도 및 장애의 정도와 밀접하게 관련되어 나타날 수 있으며, 환자가 호소하는 정서적 스트레스에 대한 포괄적인 이해와 기능장애에 대한 적절한 관리가 측두하악장애 환자의 성공적인 치료에 매우 중요하리라 생각된다.