• Structural Engineering and Mechanics
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• 제65권5호
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• pp.573-585
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• 2018

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.

• Advances in nano research
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• 제7권6호
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• pp.443-457
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• 2019

In this investigation, dynamic and bending behaviors of isolated protein microtubules are analyzed. Microtubules (MTs) can be considered as bio-composite structures that are elements of the cytoskeleton in eukaryotic cells and posses considerable roles in cellular activities. They have higher mechanical characteristics such as superior flexibility and stiffness. In the modeling purpose of microtubules according to a hollow beam element, a novel single variable sinusoidal beam model is proposed with the conjunction of modified strain gradient theory. The advantage of this model is found in its new displacement field involving only one unknown as the Euler-Bernoulli beam theory, which is even less than the Timoshenko beam theory. The equations of motion are constructed by considering Hamilton's principle. The obtained results are validated by comparing them with those given based on higher shear deformation beam theory containing a higher number of variables. A parametric investigation is established to examine the impacts of shear deformation, length scale coefficient, aspect ratio and shear modulus ratio on dynamic and bending behaviors of microtubules. It is remarked that when length scale coefficients are almost identical of the outer diameter of MTs, microstructure-dependent behavior becomes more important.

• 마이크로전자및패키징학회지
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• 제26권4호
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• pp.39-46
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• 2019

Polydimethylsiloxane (PDMS)를 베이스 기판으로 사용하고 이보다 강성도가 높은 flexible printed circuit board (FPCB)를 island 기판으로 사용하여 island-bridge 구조의 soft PDMS/hard PDMS/FPCB 신축 패키지를 형성하고, 이의 유효 탄성계수와 변형거동을 분석하였다. 각기 탄성계수가 0.28 MPa, 1.74 MPa 및 1.85 GPa인 soft PDMS, hard PDMS, FPCB를 사용하여 형성한 soft PDMS/hard PDMS/FPCB 신축 패키지의 유효 탄성계수는 0.58 MPa로 분석되었다. Soft PDMS/hard PDMS/FPCB 신축 패키지에서 soft PDMS의 변형률이 0.3이 되도록 인장시 hard PDMS와 FPCB의 변형률은 각기 0.1과 0.003이었다.

• Design & Manufacturing
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• 제7권1호
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• pp.11-18
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• 2013

This paper presents the plastic inhomogeneous deformation behavior of bimetal composite rods during the axisymmetric and steady-state extrusion process through a conical die. The rigid-plastic FE model considering frictional contact problem was used to analyze the co-extrusion process with material combinations of Cu/Al. Different cases of initial geometry shape for composite material were simulated under different conditions of co-extrusion process, which includes the interference and frictional conditions. The main design parameters influencing on deformation pattern are diameter ratio of the composite components and semi-die angle. Efforts are focused on the deformation patterns, velocity gradient, predicted forming load and the end distance through the various simulations. Simulation results indicate that there is an obvious difference of forming pattern with various diameter ratio and semi-die angle. The analysis in this paper is concentrated on the evaluation of the design parameters on the deformation pattern of composite rod.

• Structural Engineering and Mechanics
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• 제61권6호
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• pp.721-736
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• 2017

In this paper, free vibration characteristics of functionally graded (FG) nanobeams embedded on elastic medium are investigated based on third order shear deformation (Reddy) beam theory by presenting a Navier type solution for the first time. The material properties of FG nanobeam are assumed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on third order shear deformation beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. The obtained results are presented for the vibration analysis of the FG nanobeams such as the influences of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.

• Steel and Composite Structures
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• 제32권3호
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• pp.389-410
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• 2019

In this article, a simple quasi-3D shear deformation theory is employed for thermo-mechanical bending analysis of functionally graded material (FGM) sandwich plates. The displacement field is defined using only 5 variables as the first order shear deformation theory (FSDT). Unlike the other high order shear deformation theories (HSDTs), the present formulation considers a new kinematic which includes undetermined integral variables. The governing equations are determined based on the principle of virtual work and then they are solved via Navier method. Analytical solutions are proposed to provide the deflections and stresses of simply supported FGM sandwich structures. Comparative examples are presented to demonstrate the accuracy of the present theory. The effects of gradient index, geometrical parameters and thermal load on thermo-mechanical bending response of the FG sandwich plates are examined.

• 한국철도학회논문집
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• 제20권5호
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• pp.637-648
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• 2017

본 논문에서는 이전 논문에서 제시한 불연속 프리캐스트 콘크리트궤도 유한요소 해석모델과 초기 변형 및 온도 변형 분석 결과를 이용하여 초기 변형과 온도에 의한 변형이 슬래브의 응력 분포에 미치는 영향을 분석하였다. 분석 결과에 따르면 프리캐스트 콘크리트 슬래브에 이미 발생해 있는 초기 변형과 온도 경사에 의한 변형이 있는 상태에서 열차하중이 작용하는 경우에는 슬래브 중앙, 모서리 중앙, 전단포켓 코너부 등 슬래브 상부에서 최대 인장응력이 발생하게 되어 열차하중만 작용하는 경우와 매우 다른 응력 분포를 나타낸다. 따라서 불연속 프리캐스트 콘크리트 궤도의 실제 취약부의 위치와 파괴모드를 예측하기 위해서는 슬래브의 초기 변형과 온도 변형을 고려하여 열차 하중에 의한 응력을 산정해야만 한다.

• 한국정보과학회논문지:소프트웨어및응용
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• 제37권1호
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• pp.9-18
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• 2010

본 논문에서는 호기와 흡기에 촬영된 흉부 CT 영상간 폐 영상정합을 위해 데몬 알고리즘을 이용한 비강체 정합 방법을 제안한다. 먼저 두 영상에 어파인 변환을 적용하여 폐를 전역적으로 정렬한 후, 데몬 알고리즘에 기반한 비강체 정합 방법을 적용하여 지역적으로 변형시킨다. 데몬 힘의 계산을 위해 기준영상의 기울기 정보 뿐 아니라 부유영상의 기울기 정보를 함께 사용하여 기준영상의 기울기가 약한 부분에서 빠른 수렴을 돕는다. 활성-셀 기반 데몬 알고리즘은 두 영상 간 정합도가 높은 셀에서의 불필요한 변위 계산을 방지함으로써 정합 과정을 가속화시키고 변형 접힘 현상의 확률을 줄여주는 역할을 한다. 제안방법의 성능을 평가하기 위해 기준 기울기 힘을 사용한 방법과 부유 기울기 힘을 함께 사용한 방법을 비교하고, 활성-셀을 사용한 방법과 사용하지 않은 방법을 비교하였다. 실험 결과는 제안 방법이 변형이 큰 폐를 정확하게 정합하며 수행시간을 감소시킴을 보여준다.

• 한국분말재료학회지
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• 제29권5호
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• pp.382-389
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• 2022

A typical trade-off relationship exists between strength and elongation in face-centered cubic metals. Studies have recently been conducted to enhance strength without ductility reduction through surface-treatment-based ultrasonic nanocrystalline surface modification (UNSM), which creates a gradient microstructure in which grains become smaller from the inside to the surface. The transformation-induced plasticity effect in Fe-Mn alloys results in excellent strength and ductility due to their high work-hardening rate. This rate is achieved through strain-induced martensitic transformation when an alloy is plastically deformed. In this study, Fe-6%Mn powders with different sizes were prepared by high-energy ball milling and sintered through spark plasma sintering to produce Fe-6%Mn samples. A gradient microstructure was obtained by stacking the different-sized powders to achieve similar effects as those derived from UNSM. A compressive test was performed to investigate the mechanical properties, including the yielding behavior. The deformed microstructure was observed through electron backscatter diffraction to determine the effects of gradient plastic deformation.

• Structural Engineering and Mechanics
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• 제28권5호
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• pp.603-633
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• 2008

A four-node plate finite element for the analysis of laminated composites which is developed using strain gradient notation is presented. The element is based on a first-order shear deformation theory and on the equivalent lamina assumption. Strains and stresses can be calculated at different points through the thickness of the plate. They are averaged values due to the equivalent lamina assumption. A shear correction factor is used as the transverse shear strain is taken to be constant over the plate thickness while its actual variation is parabolic. Strain gradient notation, which is physically interpretable, allows for the detailed a-priori analysis of the finite element model. The polynomial expansions are inspected and spurious terms responsible for modeling errors are identified in the shear strains polynomial expansions. The element is corrected by simply removing the spurious terms from the shear strains expansions. The element is implemented into a FORTRAN finite element code in two versions; namely, with and without spurious terms. Results are compared to show the effects of the spurious terms on the solutions. It is also shown that a refined mesh composed of corrected elements provides solutions which approximate very well the analytical solutions, validating the procedure.