• 제목/요약/키워드: linear equations

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분해가 고려된 쓰레기 매립지의 장기 침하 거동 (Long -Term Settlement Behavior of Landfills with Consideration of Refuse Decomposition)

  • 박현일;이승래;고광훈
    • 한국지반공학회지:지반
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    • 제14권1호
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    • pp.5-14
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    • 1998
  • 쓰레기 매립지의 장기 침하 메카니즘은 일반적인 홀의 거동과는 달리 생물학적인 분해에 의해서 크게 영향을 받는다. 본 논문에서는 쓰레기 매립지의 장기 침하량(역학적 이차침하량과 분해에 의한 이차침하량)을 예측하기 위하여 두 식이 사용되었다. 역학적 이차침하는 변형률-대수 시간에서 선형적인 관계를 갖는다고 가정하였다. 분해에 의한 침하를 평가하기 위하여, 분해 가능한 쓰레기 고형물의 용액화에 관련된 일차반응기작으로 모사되는 가수분해 과정을 고려한 모델을 숙성된 (aged) 쓰레기로 충진된 Lysimeter 침하자료에 적용하였다. 본 연구에서는 분해과정 가운데 쓰레기 고형물의 용액화로 말미암아 유발되는 침하를 효과적으로 모사할 수 있는 간단한 수학적 모델을 제안하고자 하였다.

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균일하게 탄성지지된 보-기둥요소의 엄밀한 동적강성행렬 유도 (Derivation of Exact Dynamic Stiffness Matrix of a Beam-Column Element on Elastic Foundation)

  • 김문영;윤희택;곽태영
    • 한국전산구조공학회논문집
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    • 제15권3호
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    • pp.463-469
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    • 2002
  • 탄성지반 위에 놓인 보-기둥 요소의 총포텐셜 에너지로부터 변분원리를 적용하여 지배방정식과 힘-변위 관계식을 유도하였다. 4계 상미분방정식 형태의 지배방정식을 4개의 변위 파라메타를 도입하여 1계 연립미분방정식 형태의 선형 고유치 문제로 전환하고, 힘-변위 관계식을 적용하여 엄밀한 정적, 동적 요소강성행렬을 유도하였다. 직접강성법을 이용하여 구조물 강성행렬을 구하고, 2차원 보-기둥구조의 엄밀한 좌굴하중과 고유진동수를 구하고, 결과를 유한요소해와 비교함으로써 본 연구의 타당성을 검증하였다. 이러한 엄밀한 해석방법은 Hermitian 다항식을 형상함수로 도입하여 요소의 강성행렬을 산정하는 유한요소법과 비교할 때, 요소의 수를 대폭 줄일 수 있는 장점이 있다.

박벽 공간뼈대구조의 안정성 및 후좌굴 유한요소해석 (Stability and Post-Buckling Analyses of Thin-Walled Space Frames Using Finite Element Method)

  • 김문영;안성원
    • 전산구조공학
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    • 제10권4호
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    • pp.205-216
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    • 1997
  • 구속된 ?(restrained warping)효과를 고려하는 박벽 공간뼈대구조의 횡후좌굴거동을 조사하기 위하여 기하학적 비선형 유한요소이론 및 해석법을 제시한다. 가상일의 원리를 이용하여 대변형효과를 고려한 3차원 연속체의 평형방정식으로부터, 구속된 ?효과를 고려하고 유한한 회전각의 2차항의 효과를 포함하는 변위장을 도입하여 초기응력을 받는 박벽 공간뼈대요소의 증분평형방정식을 유도한다. 박벽 공간뼈대구조를 유한요소로 나누고 변위장을 요소변위에 관한 Hermitian 다항식으로 나타내어 이를 평형방정식에 대입함으로써 접선강도행렬을 유도한다. 또한 updated Lagrangian formulation에 근거하여, 증분변위로부터 강체회전변위와 순수변형성분을 분리시켜서 강체회전은 요소의 방향변화를 결정하고, 순수변형은 부재력증분을 산정하는 불평형하중 산정법을 제시한다. 박벽 공간뼈대구조의 횡-비틂좌굴 및 후좌굴 거동에 대한 예제들을 통하여 본 연구에 대한 해석결과와 문헌의 결과를 비교 검토함으로써 본 연구에서 제시된 이론 및 해석방법의 정당성을 입증한다.

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COMPARISONS OF PARALLEL PRECONDITIONERS FOR THE COMPUTATION OF SMALLEST GENERALIZED EIGENVALUE

  • Ma, Sang-Back;Jang, Ho-Jong;Cho, Jae-Young
    • Journal of applied mathematics & informatics
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    • 제11권1_2호
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    • pp.305-316
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    • 2003
  • Recently, an iterative algorithm for finding the interior eigenvalues of a definite matrix by CG-type method has been proposed. This method compares to the inverse power method. The given matrices A, and B are assumed to be large and sparse, and SPD( Symmetric Positive Definite) The CG scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for large sparse eigenproblems for smallest eigenvalue. Also, it is very amenable to parallel computations, like the CG method for the linear systems. A proper choice of the preconditioner significantly improves the convergence of the CG scheme. But for parallel computations we need to find an efficient parallel preconditioner. Our candidates we ILU(0) in the wave-front order, ILU(0) in the multi-coloring order, Point-SSOR(Symmetric Successive Overrelaxation), and Multi-Color Block SSOR preconditioner. Wavefront order is a simple way to increase parallelism in the natural order, and Multi-coloring realizes a parallelism of order(N), where N is the order of the matrix. Another choice is the Multi-Color Block SSOR(Symmetric Successive OverRelaxation) preconditioning. Block SSOR is a symmetric preconditioner which is expected to minimize the interprocessor communication due to the blocking. We implemented the results on the CRAY-T3E with 128 nodes. The MPI (Message Passing Interface) library was adopted for the interprocessor communications. The test problem was drawn from the discretizations of partial differential equations by finite difference methods. The results show that for small number of processors Multi-Color ILU(0) has the best performance, while for large number of processors Multi-Color Block SSOR performs the best.

Large deflection behavior and stability of slender bars under self weight

  • Goncalves, Paulo B.;Jurjo, Daniel Leonardo B.R.;Magluta, Carlos;Roitman, Ney;Pamplona, Djenane
    • Structural Engineering and Mechanics
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    • 제24권6호
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    • pp.709-725
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    • 2006
  • In this paper the buckling and post-buckling behavior of slender bars under self-weight are studied. In order to study the post-buckling behavior of the bar, a geometrically exact formulation for the non-linear analysis of uni-directional structural elements is presented, considering arbitrary load distribution and boundary conditions. From this formulation one obtains a set of first-order coupled nonlinear equations which, together with the boundary conditions at the bar ends, form a two-point boundary value problem. This problem is solved by the simultaneous use of the Runge-Kutta integration scheme and the Newton-Raphson method. By virtue of a continuation algorithm, accurate solutions can be obtained for a variety of stability problems exhibiting either limit point or bifurcational-type buckling. Using this formulation, a detailed parametric analysis is conducted in order to study the buckling and post-buckling behavior of slender bars under self-weight, including the influence of boundary conditions on the stability and large deflection behavior of the bar. In order to evaluate the quality and accuracy of the results, an experimental analysis was conducted considering a clamped-free thin-walled metal bar. As this kind of structure presents a high index of slenderness, its answers could be affected by the introduction of conventional sensors. In this paper, an experimental methodology was developed, allowing the measurement of static or dynamic displacements without making contact with the structure, using digital image processing techniques. The proposed experimental procedure can be used to a wide class of problems involving large deflections and deformations. The experimental buckling and post-buckling behavior compared favorably with the theoretical and numerical results.

Prediction of the turning and zig-zag maneuvering performance of a surface combatant with URANS

  • Duman, Suleyman;Bal, Sakir
    • Ocean Systems Engineering
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    • 제7권4호
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    • pp.435-460
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    • 2017
  • The main objective of this study is to investigate the turning and zig-zag maneuvering performance of the well-known naval surface combatant DTMB (David Taylor Model Basin) 5415 hull with URANS (Unsteady Reynolds-averaged Navier-Stokes) method. Numerical simulations of static drift tests have been performed by a commercial RANS solver based on a finite volume method (FVM) in an unsteady manner. The fluid flow is considered as 3-D, incompressible and fully turbulent. Hydrodynamic analyses have been carried out for a fixed Froude number 0.28. During the analyses, the free surface effects have been taken into account using VOF (Volume of Fluid) method and the hull is considered as fixed. First, the code has been validated with the available experimental data in literature. After validation, static drift, static rudder and drift and rudder tests have been simulated. The forces and moments acting on the hull have been computed with URANS approach. Numerical results have been applied to determine the hydrodynamic maneuvering coefficients, such as, velocity terms and rudder terms. The acceleration, angular velocity and cross-coupled terms have been taken from the available experimental data. A computer program has been developed to apply a fast maneuvering simulation technique. Abkowitz's non-linear mathematical model has been used to calculate the forces and moment acting on the hull during the maneuvering motion. Euler method on the other hand has been applied to solve the simultaneous differential equations. Turning and zig-zag maneuvering simulations have been carried out and the maneuvering characteristics have been determined and the numerical simulation results have been compared with the available data in literature. In addition, viscous effects have been investigated using Eulerian approach for several static drift cases.

반개착식 터널 공법에 관한 수치 해석적 연구 (Numerical analysis for semi cut and cover tunnelling method)

  • 노병국;박종관;백승규
    • 한국터널지하공간학회 논문집
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    • 제15권2호
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    • pp.113-122
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    • 2013
  • 최근 터널 갱구부와 저토피 구간에 대한 환경 친화적인 터널공법에 대한 관심이 증가하고 있다. 콘크리트 슬래브를 이용한 반개착식 터널공법을 적용한 연구 및 시공사례가 증가하고 있으나, 하중조합 및 아치콘크리트의 단면에 대한 별도의 적용 기준이 없다. 따라서 본 연구에서는 반개착식 공법에 대한 기준을 제시하기 위하여 지반조건과, 터널 상부 지층 두께, 되메움 두께, 상부지반 지표면의 경사 각도를 변화시키는 등의 다양한 조건들에 대하여 수치해석을 수행하였다. 수치해석 결과들을 회귀분석법으로 분석하고, 유도된 회귀 분석식을 분류하고 정리하여 합리적이고, 경제적이며, 안전한 반개착식 터널 굴착 공법의 기준을 제안하고자 하였다.

질소 이온 발광 분광법을 이용한 초음속 유동의 기체 온도 측정 (Gas Temperature Measurement in Supersonic Flows by N2+ Emission Spectroscopy)

  • 신지철
    • 대한기계학회논문집B
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    • 제34권3호
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    • pp.245-250
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    • 2010
  • 초음속 유동에서의 공기 방전에 대한 기체 (회전) 온도를 측정하는 과정이 자세하게 소개되었다. 초음속 유동에서는 직접적인 온도 측정이 어려우므로 질소 분자 이온 스펙트럼의 광학적 발광 분광법을 이용하는 비침투 방식의 측정법이 사용되었다. 질소 분자 이온의 발광 스펙트럼 구조를 이해하기 위하여 발광선의 세기를 나타내는 관계식들에 대한 자세한 설명이 소개되었다. 유도된 발광 스펙트럼의 표현식을 이용하여 질소 이온의 first negative system을 구현하였고 실험으로 측정된 스펙트럼과 비교하였다. 합성 스펙트럼과 측정된 스펙트럼들은 밴드 스펙트럼 전 범위에 걸쳐서 6-8%의 상대오차 이내로 서로 일치함을 보여주었다. 마하 3의 초음속 경계층에서 25 mA의 직류 방전에 의한 기체 온도 분포 곡선을 측정한 결과 온도값이 최대 약 350 K인 선형적인 변화를 보여주었다.

Determination of global ice loads on the ship using the measured full-scale motion data

  • Lee, Jae-Man;Lee, Chun-Ju;Kim, Young-Shik;Choi, Gul-Gi;Lew, Jae-Moon
    • International Journal of Naval Architecture and Ocean Engineering
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    • 제8권4호
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    • pp.301-311
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    • 2016
  • This paper describes the whole procedures to determine ice-induced global loads on the ship using measured full-scale data in accordance with the method proposed by the Canadian Hydraulics Centre of the National Research Council of Canada. Ship motions of 6 degrees of freedom (dof) are found by processing the commercial sensor signals named Motion Pak II under the assumption of rigid body motion. Linear accelerations as well as angular rates were measured by Motion Pak II data. To eliminate the noise of the measured data and the staircase signals due to the resolution of the sensor, a band pass filter that passes frequencies between 0.001 and 0.6 Hz and cubic spline interpolation resampling had been applied. 6 dof motions were computed by the integrating and/or differentiating the filtered signals. Added mass and damping force of the ship had been computed by the 3-dimensional panel method under the assumption of zero frequency. Once the coefficients of hydrodynamic and hydrostatic data as well as all the 6 dof motion data had been obtained, global ice loads can be computed by solving the fully coupled 6 dof equations of motion. Full-scale data were acquired while the ARAON rammed old ice floes in the high Arctic. Estimated ice impact forces for two representative events showed 7e15 MN when ship operated in heavy ice conditions.

Envelope-Function Equation and Motion of Wave Packet in a Semiconductor Superlattice Structure

  • Kim, Byoung-Whi;Jun, Young-Il;Jung, Hee-Bum
    • ETRI Journal
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    • 제21권1호
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    • pp.1-27
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    • 1999
  • We present a new description of envelope-function equation of the superlattice (SL). The SL wave function and corresponding effective-mass equation are formulated in terms of a linear combination of Bloch states of the constituent material with smaller band gap. In this envelope-function formalism, we review the fundamental concept on the motion of a wave packet in the SL structure subjected to steady and uniform electric fields F. The review confirms that the average of SL crystal momentums K = ($k_x,k_y,q$), where ($K_x,k_y$) are bulk inplane wave vectors and q SL wave vector, included in a wave packet satisfies the equation of motion = $_0+Ft/h$; and that the velocity and acceleration theorems provide the same type of group velocity and definition of the effective mass tensor, respectively, as in the Bulk. Finally, Schlosser and Marcus's method for the band theory of metals has been by Altarelli to include the interface-matching condition in the variational calculation for the SL structure in the multi-band envelope-function approximation. We re-examine this procedure more thoroughly and present variational equations in both general and reduced forms for SLs, which agrees in form with the proposed envelope-function formalism. As an illustration of the application of the present work and also for a brief investigation of effects of band-parameter difference on the subband energy structure, we calculate by the proposed variational method energies of non-strained $GaAs/Al_{0.32}Ga_{0.68}As$ and strained $In_{0.63}Ga_{0.37}As/In_{0.73}Ga_{0.27}As_{0.58}P_{0.42}SLs$ with well/barrier widths of $60{\AA}/500{\AA}$ and 30${\AA}/30{\AA}$, respectively.

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