• 제목/요약/키워드: variational method

검색결과 595건 처리시간 0.025초

Combined multi-predict-correct iterative method for interaction between pulsatile flow and large deformation structure

  • Wang, Wenquan;Zhang, Li-Xiang;Yan, Yan;Guo, Yakun
    • Coupled systems mechanics
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    • 제1권4호
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    • pp.361-379
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    • 2012
  • This paper presents a fully coupled three-dimensional solver for the analysis of interaction between pulsatile flow and large deformation structure. A partitioned time marching algorithm is employed for the solution of the time dependent coupled discretised problem, enabling the use of highly developed, robust and well-tested solvers for each field. Conservative transfer of information at the fluid-structure interface is combined with an effective multi-predict-correct iterative scheme to enable implicit coupling of the interacting fields at each time increment. The three-dimensional unsteady incompressible fluid is solved using a powerful implicit time stepping technique and an ALE formulation for moving boundaries with second-order time accurate is used. A full spectrum of total variational diminishing (TVD) schemes in unstructured grids is allowed implementation for the advection terms and finite element shape functions are used to evaluate the solution and its variation within mesh elements. A finite element dynamic analysis of the highly deformable structure is carried out with a numerical strategy combining the implicit Newmark time integration algorithm with a Newton-Raphson second-order optimisation method. The proposed model is used to predict the wave flow fields of a particular flow-induced vibrational phenomenon, and comparison of the numerical results with available experimental data validates the methodology and assesses its accuracy. Another test case about three-dimensional biomedical model with pulsatile inflow is presented to benchmark the algorithm and to demonstrate the potential applications of this method.

K-means 알고리즘을 이용한 계층적 클러스터링에서의 클러스터 계층 깊이 선택 (Selection of Cluster Hierarchy Depth in Hierarchical Clustering using K-Means Algorithm)

  • 이원휘;이신원;정성종;안동언
    • 대한전자공학회논문지SD
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    • 제45권2호
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    • pp.150-156
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    • 2008
  • 정보통신의 기술이 발달하면서 정보의 양이 많아지고 사용자의 질의에 대한 검색 결과 리스트도 많이 추출되므로 빠르고 고품질의 문서 클러스터링 알고리즘이 중요한 역할을 하고 있다. 많은 논문들이 계층적 클러스터링 방법을 이용하여 좋은 성능을 보이지만 시간이 많이 소요된다. 반면 K-means 알고리즘은 시간 복잡도를 줄일 수 있는 방법이다. 본 논문에서는 계층적 클러스터링 시스템인 콘도르(Condor) 시스템에서 K-Means 알고리즘을 이용하여 효율적으로 정보 검색을 하고 검색결과를 계층적으로 볼 수 있도록 구현하였다. 이 시스템은 K-Means Algorithm을 이용하였으며 클러스터 계층 깊이와 초기값을 조절하여 더 나은 성능을 보임을 알 수 있다.

연속용융 도금라인 용 고내침식 Fe계 합금 개발 (Development of High Erosion Resistant Fe-based Alloy for Continuous Hot Dipping Line)

  • 백민숙;김용철;백경철;곽준섭;윤동주
    • 한국표면공학회지
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    • 제53권3호
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    • pp.95-103
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    • 2020
  • In this study, the material used in the hot dip galvanizing equipment was poorly corrosion-resistant, so it was performed to solve the cost and time problems caused by equipment replacement. The theoretical calculation was performed using the DV-Xα method(Discrete Variational Local-density approximation method). The alloy (STS4XX series) of the equipment currently used has a martensite phase. Therefore, the theoretical calculation was performed by applying P4 / mmm, which is a tetragonal structure. The new alloy was chosen by designing theoretical values close to existing materials. Considering elements that contribute to corrosion, most have high prices. Therefore, the design was completed by adjusting the content using only the components of the reference material in the theoretical design. The final design alloys were chosen as D6 and D9. Designed D6 and D9 were dissolved and prepared using an induction furnace. After the heat treatment process was completed, the corrosion rate of the alloys was confirmed by using the potentiodynamic polarization test. The surface of the prepared alloys were processed horizontally and then polished to # 1200 using sand paper to perform potentiodynamic polarization test. Domestic products: 4.735 mpy (mils / year), D6: 0.9166 mpy, D9: 0.3372 mpy, alloys designed than domestic products had a lower corrosion rate. Therefore, the designed alloy was expected to have better erosion resistance.

Free vibration analysis of combined system with variable cross section in tall buildings

  • Jahanshahia, Mohammad Reza;Rahgozar, Reza
    • Structural Engineering and Mechanics
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    • 제42권5호
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    • pp.715-728
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    • 2012
  • This paper deals with determining the fundamental frequency of tall buildings that consist of framed tube, shear core, belt truss and outrigger systems in which the framed tube and shear core vary in size along the height of the structure. The effect of belt truss and outrigger system is modeled as a concentrated rotational linear spring at the belt truss and outrigger system location. Many cantilevered tall structures can be treated as cantilevered beams with variable cross-section in free vibration analysis. In this paper, the continuous approach, in which a tall building is replaced by an idealized cantilever continuum representing the structural characteristics, is employed and by using energy method and Hamilton's variational principle, the governing equation for free vibration of tall building with variable distributed mass and stiffness is obtained. The general solution of governing equation is obtained by making appropriate selection for mass and stiffness distribution functions. By applying the separation of variables method for time and space, the governing partial differential equation of motion is reduced to an ordinary differential equation with variable coefficients with the assumption that the transverse displacement is harmonic. A power-series solution representing the mode shape function of tall building is used. Applying boundary conditions yields the boundary value problem; the frequency equation is established and solved through a numerical process to determine the natural frequencies. Computer program has been developed in Matlab (R2009b, Version 7.9.0.529, Mathworks Inc., California, USA). A numerical example has been solved to demonstrate the reliability of this method. The results of the proposed mathematical model give a good understanding of the structure's dynamic characteristics; it is easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary design stages.

Stochastic fracture behavior analysis of infinite plates with a separate crack and a hole under tensile loading

  • Khubi Lal Khatri;Kanif Markad
    • Computers and Concrete
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    • 제32권1호
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    • pp.99-117
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    • 2023
  • The crack under the influence of the higher intensities of the stresses grows and the structure gets collapsed with the time when the crack length reaches to critical value. Therefore, the fracture behavior of a structure in terms of stress intensity factors (SIF) becomes important to determine the remaining fracture strength and capacity of material and structure for avoiding catastrophic failure, increasing safety and further improvement in the design. The robustness of the method has been demonstrated by comparing the numerical results with analytical and experimental results of some problems. XFEM is used to model cracks and holes in structures and predict their strength and reliability under service conditions. Further, XFEM is extended with a stochastic method for predicting the sensitivity in terms of output COVs and fracture strength in terms of mean values of stress intensity factors (SIFs) of a structure with discontinuities (cracks and holes) under tensile loading condition with input individual and combined randomness in different system parameters. In stochastic technique, the second order perturbation technique (SOPT) has been used for the predicting the fracture behavior of the structures. The stochastic/perturbation technique is also known as Taylor series expansion method and it provides the reliable results if the input randomness is less than twenty percentage. From the present numerical analysis it is observed that, the crack tip near to the hole is under the influence of the stress concentration and the variational effect of the input random parameters on the crack tip in terms of the SIFs are lesser so the COVs are the less sensitive. The COVs of mixed mode SIFs are the most sensitive for the crack angles (α=45° to 90°) for all the values of c1 and d1. The plate with the shorter distance between hole and crack is the most sensitive with all the crack angles but the crack tip which is much nearer to the hole has the highest sensitivity.

이온교환형 리튬망간산화물의 리튬이온 용출특성 및 전자상태 (Li+ Extraction Reactions with Ion-exchange type Lithium Manganese Oxide and Their Electronic Structures)

  • 김양수;정강섭;이재천
    • 한국재료학회지
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    • 제12권11호
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    • pp.860-864
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    • 2002
  • $Li^{+}$ extraction reactions with ion-exchange type lithium manganese oxide in an aqueous phase were examined using chemical and x-ray diffraction (XRD) analysis. In the process of extraction reaction, the lithium manganese oxide showed a topotactic extraction of $Li^{+ }$ in the aqueous phase mainly through an ion-exchange mechanism, and the $Li^{+}$ extracted samples indicated a high selectivity and a large capacity for $Li^{+}$ . The electronic structures and chemical bonding properties were also studied using a discrete variational (DV)-X$\alpha$ molecular orbital method with cluster model of (Li$Mn_{12}$ $O_{40}$ )$^{27-}$ for tetrahedral sites and ($Li_{7}$ Mn $O_{38}$ )$^{3}$ for octahedral site in $Li_{1.33}$ $Mn_{1.67}$ / $O_{4}$ respectively. Li in the manganese oxides is highly ionized in both sites, but the net charge of Li was greater for tetrahedral sites than octahedral. These calculations suggest that the tetrahedral sites have higher $Li^{+}$ $H^{+}$ exchangeability than the octahedral sites, and are preferable for the selective adsorption for L $i^{+}$ ions.s.

협대역 단일 주파수 신호 환경에서 일반 상호 상관 시간 지연 추정 향상을 위한 전처리기 연구 (Study on the pre-processors to improve the generalized-cross-correlation based time delay estimation under the narrow band single tone signal environments)

  • 임준석;김성일
    • 한국음향학회지
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    • 제39권3호
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    • pp.207-215
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    • 2020
  • 두 개 수신기에 도래한 신호 간의 시간 지연을 추정 방법에는 여러 가지가 존재한다. 그 중에서 두 수신기에 입력되는 서로 다른 신호간의 상호 상관으로부터 상대적인 지연을 추정하는 Generalized Cross Correlation(GCC) 방법은 안정적인 성능을 내는 전통적으로 유명한 방법이다. 그러나 GCC 방법은 단일 주파수 신호를 사용하는 경우에 일반 광대역 신호를 사용하였을 때보다 더 높은 신호 대 잡음비에서부터 추정 성능이 저하된다. 본 논문에서는 이 같은 현상을 개선하기 위해서 협대역 단일 주파수 신호에 대해 GCC를 위한 네 가지 전 처리기를 살펴본다. 시뮬레이션을 통해서 처리기를 사용하였을 때가 전 처리기를 전혀 사용하지 않았을 때보다 100 msec 길이 송신 신호에 대해서 최대 9 dB의 성능 이득을 얻었고, 1 s 길이 송신 신호에 대해서는 최대 4 dB의 성능 이득이 있음을 보인다.

Modelling of graded rectangular micro-plates with variable length scale parameters

  • Aghazadeh, Reza;Dag, Serkan;Cigeroglu, Ender
    • 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.

판으로 나뉘어진 2차원 충류 채널유동에서 동적 유체-구조물 상호작용 수치해석 (Computation of Dynamic Fluid-Structure Interaction in a 2-Dimensional Laminar Channel Flow Divided by a Plate)

  • 남궁각;최형권;유정열
    • 대한기계학회논문집B
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    • 제26권12호
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    • pp.1738-1746
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    • 2002
  • In the FSI (Fluid-Structure Interaction) problems, two different governing equations are to be solved together. One is fur the fluid and the other for the structure. Furthermore, a kinematic constraint should be imposed along the boundary between the fluid and the structure. We use the combined formulation, which incorporates both the fluid and structure equations of motion into a single coupled variational equation so that it is not necessary to calculate the fluid force on the surface of structure explicitly when solving the equations of motion of the structure. A two-dimensional channel flow divided by a Bernoulli-Euler beam is considered and the dynamic response of the beam under the influence of channel flow is studied. The Navier-Stokes equations are solved using a P2P1 Galerkin finite element method with ALE (Arbitrary Lagrangian-Eulerian) algorithm. The internal structural damping effect is not considered in this study and numerical results are compared with a previous work fer steady case. In addition to the Reynolds number, two non-dimensional parameters, which govern this fluid-structure system, are proposed. It is found that the larger the dynamic viscosity and density of the fluid are, the larger the damping of the beam is. Also, the added mass is found to be linearly proportional to the density of the fluid.

면내회전자유도를 갖는 4절점 곡면 쉘요소 (A Four-node General Shell Element with Drilling DOFs)

  • 정근영;김재민;이은행
    • 한국지진공학회논문집
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    • 제16권4호
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    • pp.37-52
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    • 2012
  • 이 연구에서는 감절점쉘요소의 개념에 근거한 새로운 4절점 곡면 쉘요소를 제시하였다. 회전장이 독립변수로 도입된 범함수에 의하여 면내회전자유도를 도입함으로써 개발된 쉘요소에서는 절점당 6자유도를 갖도록 하였다. 아울러 쉘요소의 면내거동 개선을 위하여 4개의 비적합변위형에 의한 비적합변위를 면내방향의 변위성분에 추가하였으며, 면외거동 개선을 위하여 대체전단변형률장이 적용되었다. 이 연구에서의 비적합변위형의 수치적 구현에 있어서 일정한 변형률상태를 표현할 수 있도록 하기 위하여 비적합변위형의 직접 수정법이 적용되었다. 이렇게 정식화된 쉘요소 강성행렬의 수치적분에 있어서는 부피적분을 위하여 9점 적분법이 사용되었다. 개발된 쉘요소는 바람직하지 못한 영에너지모드를 갖지 않으며, 일정한 변형률 상태를 표현할 수 있음을 확인하였다. 개발된 4절점 곡면 쉘 요소에 대한 다양한 수치예제를 통한 검증 결과, 전반적으로 양호한 거동을 보여주고 있음을 확인하였다.