• Title/Summary/Keyword: Linear Curvature

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Bonding Property of Silicon Wafer Pairs with Annealing Method (열처리 방법에 따른 실리콘 기판쌍의 접합 특성)

  • 민홍석;이상현;송오성;주영창
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.16 no.5
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    • pp.365-371
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    • 2003
  • We prepared silicon on insulator(SOI) wafer pairs of Si/1800${\AA}$ -SiO$_2$ ∥ 1800${\AA}$ -SiO$_2$/Si using water direct bonding method. Wafer pairs bonded at room-temperature were annealed by a normal furnace system or a fast linear annealing(FLA) equipment, and the micro-structure of bonding interfaces for each annealing method was investigated. Upper wafer of bonded pairs was polished to be 50 $\mu\textrm{m}$ by chemical mechanical polishing(CMP) process to confirm the real application. Defects and bonding area of bonded water pairs were observed by optical images. Electrical and mechanical properties were characterized by measuring leakage current for sweeping to 120 V, and by observing the change of wafer curvature with annealing process, respectively. FLA process was superior to normal furnace process in aspects of bonding area, I-V property, and stress generation.

Shape Design Optimization using Isogeometric Analysis Method (등기하 해석법을 이용한 형상 최적 설계)

  • Ha, Seung-Hyun;Cho, Seon-Ho
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2008.04a
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    • pp.216-221
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    • 2008
  • Shape design optimization for linear elasticity problem is performed using isogeometric analysis method. In many design optimization problems for real engineering models, initial raw data usually comes from CAD modeler. Then designer should convert this CAD data into finite element mesh data because conventional design optimization tools are generally based on finite element analysis. During this conversion there is some numerical error due to a geometry approximation, which causes accuracy problems in not only response analysis but also design sensitivity analysis. As a remedy of this phenomenon, the isogeometric analysis method is one of the promising approaches of shape design optimization. The main idea of isogeometric analysis is that the basis functions used in analysis is exactly same as ones which represent the geometry, and this geometrically exact model can be used shape sensitivity analysis and design optimization as well. In shape design sensitivity point of view, precise shape sensitivity is very essential for gradient-based optimization. In conventional finite element based optimization, higher order information such as normal vector and curvature term is inaccurate or even missing due to the use of linear interpolation functions. On the other hands, B-spline basis functions have sufficient continuity and their derivatives are smooth enough. Therefore normal vector and curvature terms can be exactly evaluated, which eventually yields precise optimal shapes. In this article, isogeometric analysis method is utilized for the shape design optimization. By virtue of B-spline basis function, an exact geometry can be handled without finite element meshes. Moreover, initial CAD data are used throughout the optimization process, including response analysis, shape sensitivity analysis, design parameterization and shape optimization, without subsequent communication with CAD description.

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The effect of impact with adjacent structure on seismic behavior of base-isolated buildings with DCFP bearings

  • Bagheri, Morteza;Khoshnoudiana, Faramarz
    • Structural Engineering and Mechanics
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    • v.51 no.2
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    • pp.277-297
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    • 2014
  • Since the isolation bearings undergo large displacements in base-isolated structures, impact with adjacent structures is inevitable. Therefore, in this investigation, the effect of impact on seismic response of isolated structures mounted on double concave friction pendulum (DCFP) bearings subjected to near field ground motions is considered. A non-linear viscoelastic model of collision is used to simulate structural pounding more accurately. 2-, 4- and 8-story base-isolated buildings adjacent to fixed-base structures are modeled and the coupled differential equations of motion related to these isolated systems are solved in the MATLAB environment using the SIMULINK toolbox. The variation of seismic responses such as base shear, displacement in the isolation system and superstructure (top floor) is computed to study the impact condition. Also, the effects of variation of system parameters: isolation period, superstructure period, size of seismic gap between two structures, radius of curvature of the sliding surface and friction coefficient of isolator are contemplated in this study. It is concluded that the normalized base shear, bearing and top floor displacement increase due to impact with adjacent structure. When the distance between two structures decreases, the base shear and displacement increase comparing to no impact condition. Besides, the increase in friction coefficient difference also causes the normalized base shear and displacement in isolation system and superstructure increase in comparison with bi-linear hysteretic behavior of base isolation system. Totally, the comparison of results indicates that the changes in values of friction coefficient have more significant effects on 2-story building than 4- and 8-story buildings.

Wave load resistance of high strength concrete slender column subjected to eccentric compression

  • Jayakumar, M.;Rangan, B.V.
    • Structural Engineering and Mechanics
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    • v.50 no.3
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    • pp.287-304
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    • 2014
  • A computer based iterative numerical procedure has been developed to analyse reinforced high strength concrete columns subjected to horizontal wave loads and eccentric vertical load by taking the material, geometrical and wave load non-linearity into account. The behaviour of the column has been assumed, to be represented by Moment-Thrust-Curvature relationship of the column cross-section. The formulated computer program predicts horizontal load versus deflection behaviour of a column up to failure. The developed numerical model has been applied to analyse several column specimens of various slenderness, structural properties and axial load ratios, tested by other researchers. The predicted values are having a better agreement with experimental results. A simplified user friendly hydrodynamic load model has been developed based on Morison equation supplemented with a wave slap term to predict the high frequency non-linear impulsive hydrodynamic loads arising from steep waves, known as ringing loads. A computer program has been formulated based on the model to obtain the wave loads and non-dimensional wave load coefficients for all discretised nodes, along the length of column from instantaneous free water surface to bottom of the column at mud level. The columns of same size and material properties but having different slenderness ratio are analysed by the developed numerical procedure for the simulated wave loads under various vertical thrust. This paper discusses the results obtained in detail and effect of slenderness in resisting wave loads under various vertical thrust.

Welding Deformation Analysis of Plates Using the Inherent Strain-based Equivalent Load Method (고유변형률 기반 등가하중법을 이용한 판의 용접변형 해석)

  • Lee, Joo-Sung
    • Journal of Welding and Joining
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    • v.28 no.2
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    • pp.39-46
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    • 2010
  • IIn this study, used is the equivalent loading method based on the inherent strain to predict the welding deformation of panel members. Equivalent loads are computed from the inherent strain distribution around weld line, and then applied for the linear finite element analysis. Thermal deformation of panel members can be, of course, carried out through the rigorous thermal elasto-plastic analysis procedure but it is not practical in applying to predicting the welding deformation of large structures such as blocks found in a ship structure from view of computing time. The present equivalent load approach has been applied to flat plate model to verify the present approach, and to several curved plate models having the curvature in the welding direction to investigate the effect of the longitudinal curvature upon the weld-induced deformation. The results are compared with those by thermal elasto-plastic analysis. As far as the present results are concerned, it can be said that the present approach shows good agreement with the results by welding experiment and the rigorous thermal elasto-plastic analysis. The present approach has been also applied to predict the welding deformation of panel block as for application illustration to practical model.

Kinetics and Mechanism of Azidolysis of Y-Substituted Phenyl Benzoates

  • Um, Ik-Hwan;Kim, Eun-Hee;Han, Hyun-Joo
    • Bulletin of the Korean Chemical Society
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    • v.29 no.3
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    • pp.580-584
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    • 2008
  • Second-order rate constants (kN) have been measured spectrophotometrically for reactions of Y-substituted phenyl benzoates (1a-h) with azide ion (N3) in 80 mol % H2O/20 mol % DMSO at 25.0 0.1 oC. The Brnsted-type plot for the azidolysis exhibits a downward curvature, i.e., the slope (b lg) changes from 0.97 to 0.20 as the basicity of the leaving group decreases. The pKao (defined as the pKa at the center of the Brnsted curvature) is 4.8, which is practically identical to the pKa of the conjugate acid of N3 ion (4.73). Hammett plots correlated with s o and s constants exhibit highly scattered points for the azidolysis. On the contrary, the corresponding Yukawa-Tsuno plot results in an excellent linear correlation with r = 2.45 and r = 0.40, indicating that the leaving group departs in the rate-determining step. The curved Brnsted-type plot has been interpreted as a change in the rate-determining step in a stepwise mechanism. The microscopic rate constants (k1 and k2/k1 ratio) have been calculated for the azidolysis and found to be consistent with the proposed mechanism.

Aminolysis of Y-Substituted Phenyl 2-Thiophenecarboxylates and 2-Furoates: Effect of Modification of Nonleaving Group from 2-Furoyl to 2-Thiophenecarbonyl on Reactivity and Mechanism

  • Um, Ik-Hwan;Min, Se-Won
    • Bulletin of the Korean Chemical Society
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    • v.29 no.3
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    • pp.585-589
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    • 2008
  • Second-order rate constants (kN) have been measured for reactions of Y-substituted phenyl 2-thiophenecarboxylates (6a-h) with morpholine and piperidine in 80 mol % H2O/20 mol % DMSO at 25.0 0.1 oC. The Brnsted-type plot for the reactions of 6a-h with morpholine is linear with b lg = 1.29, indicating that the reactions proceed through a tetrahedral zwitterionic intermediate (T?). On the other hand, the Brnsted-type plot for the reactions of 6a-h with piperidine exhibits a downward curvature, implying that a change in the rate-determining step occurs on changing the substituent Y in the leaving group. Dissection of kN into microscopic rate constants (i.e., k1 and k2/k1 ratio) has revealed that k1 is smaller for the reactions of 6a-h than for those of Y-substituted phenyl 2-furoates (5a-h), while the k2/k1 ratio is almost the same for the reactions of 5a-h and 6a-h. It is also reported that modification of the nonleaving group from the furoyl (5a-h) to the thiophenecarbonyl (6a-h) does not influence pKao (defined as the pKa at the center of the Brnsted curvature) as well as the k2/k1 ratio.

Concave Surface Boundary Layer Flows in the Presence of Streamwise Vortices

  • Winoto, Sonny H.;Tandiono, Tandiono;Shah, Dilip A.;Mitsudharmadi, Hatsari
    • International Journal of Fluid Machinery and Systems
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    • v.4 no.1
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    • pp.33-46
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    • 2011
  • Concave surface boundary-layer flows are subjected to centrifugal instability which results in the formation of streamwise counter-rotating vortices. Such boundary layer flows have been experimentally investigated on concave surfaces of 1 m and 2 m radius of curvature. In the experiments, to obtain uniform vortex wavelengths, thin perturbation wires placed upstream and perpendicular to the concave surface leading edge, were used to pre-set the wavelengths. Velocity contours were obtained from hot-wire anemometer velocity measurements. The most amplified vortex wavelengths can be pre-set by the spanwise spacing of the thin wires and the free-stream velocity. The velocity contours on the cross-sectional planes at several streamwise locations show the growth and breakdown of the vortices. Three different vortex growth regions can be identified. The occurrence of a secondary instability mode is also shown as mushroom-like structures as a consequence of the non-linear growth of the streamwise vortices. Wall shear stress measurements on concave surface of 1 m radius of curvature reveal that the spanwise-averaged wall shear stress increases well beyond the flat plate boundary layer values. By pre-setting much larger or much smaller vortex wavelength than the most amplified one, the splitting or merging of the streamwise vortices will respectively occur.

Shape Design Sensitivity Analysis using Isogeometric Approach (CAD 형상을 활용한 설계 민감도 해석)

  • Ha, Seung-Hyun;Cho, Seon-Ho
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2007.04a
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    • pp.577-582
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    • 2007
  • A variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions in analysis domain arc generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Thus. the solution space can be represented in terms of the same functions to represent the geometry. The coefficients of basis functions or the control variables play the role of degrees-of-freedom. Furthermore, due to h-. p-, and k-refinement schemes, the high order geometric features can be described exactly and easily without tedious re-meshing process. The isogeometric sensitivity analysis method enables us to analyze arbitrarily shaped structures without re-meshing. Also, it provides a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling. To obtain precise shape sensitivity, the normal and curvature of boundary should be taken into account in the shape sensitivity expressions. However, in conventional finite element methods, the normal information is inaccurate and the curvature is generally missing due to the use of linear interpolation functions. A continuum-based adjoint sensitivity analysis method using the isogeometric approach is derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of boundary. In isogeometric analysis, however, the geometric properties arc already embedded in the B-spline shape functions and control points. The perturbation of control points in isogeometric analysis automatically results in shape changes. Using the conventional finite clement method, the inter-element continuity of the design space is not guaranteed so that the normal vector and curvature arc not accurate enough. On tile other hand, in isogeometric analysis, these values arc continuous over the whole design space so that accurate shape sensitivity can be obtained. Through numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.

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Mesh Simplification Algorithm Using Differential Error Metric (미분 오차 척도를 이용한 메쉬 간략화 알고리즘)

  • 김수균;김선정;김창헌
    • Journal of KIISE:Computer Systems and Theory
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    • v.31 no.5_6
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    • pp.288-296
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    • 2004
  • This paper proposes a new mesh simplification algorithm using differential error metric. Many simplification algorithms make use of a distance error metric, but it is hard to measure an accurate geometric error for the high-curvature region even though it has a small distance error measured in distance error metric. This paper proposes a new differential error metric that results in unifying a distance metric and its first and second order differentials, which become tangent vector and curvature metric. Since discrete surfaces may be considered as piecewise linear approximation of unknown smooth surfaces, theses differentials can be estimated and we can construct new concept of differential error metric for discrete surfaces with them. For our simplification algorithm based on iterative edge collapses, this differential error metric can assign the new vertex position maintaining the geometry of an original appearance. In this paper, we clearly show that our simplified results have better quality and smaller geometry error than others.