• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2000년도 춘계학술대회논문집B
• /
• pp.282-289
• /
• 2000

Direct numerical solution for flow and heat transfer for Benard convection with a body is obtained using an accurate and efficient Fourier-Chebyshev collocation and multi-domain method. The flow and temperature fields are obtained fur different Rayleigh numbers and thermal boundary conditions of body. The body has adiabatic and constant temperature conditions. The existence of a body gives different flow and heat transfer fields in the system, compared to pure Benard convection. The flow and temperature fields are also affected by the thermal boundary condition of a body.

• 한국전산유체공학회지
• /
• 제14권4호
• /
• pp.93-100
• /
• 2009

The gridless (or meshfree) methods, such as MPS, SPH, FPM an so forth, are feasible and robust for the problems with moving boundary and/or complicated boundary shapes, because these methods do not need to generate a grid system. In this study, a gridless solver, which is based on the combination of moving least square interpolations on a cloud of points with point collocation for evaluating the derivatives of governing equations, is presented for two-dimensional unsteady incompressible Navier-Stokes problem in the low Reynolds number. A MAC-type algorithm was adopted and the Poission equation for the pressure was solved successively in the moving least square sense. Some typical problems were solved by the presented solver for the validation and the results obtained were compared with analytic solutions and the numerical results by conventional CFD methods, such as a FVM.

• 한국지반환경공학회 논문집
• /
• 제10권6호
• /
• pp.135-141
• /
• 2009

수압파쇄기술은 주로 지열, 석유, 가스 추출 시 지반의 투수성을 증가시키기 위해 사용되는 공법으로 자연에서 생성된 수압파쇄균열의 원리를 적용함으로써 실제 설계기법을 발전시켜 나아가고 있다. 본 논문에서는 균열간 거리가 아주 근접한 다중으로 분할 생성된 자연 수압파쇄균열을 대상으로 균열간 기계적 상호작용의 영향을 평가하였다. 균열의 수는 71개이며 여기에 사용된 균열폭 자료는 3,339개로 균열간 아주 근접하여 생성 당시 상당한 기계적 상호작용이 예상되었던 균열이다. 이러한 상호작용을 정량적으로 평가하기 위해서 경계병치법을 사용하였으며 측정된 균열폭에 가까운 형상을 얻기 위해 최소자승법을 통한 압력(net pressure)을 계산하였다. 그 결과 상호작용을 고려한 경우 단 2개의 압력변수만으로도 측정치에 가까운 균열폭을 얻을 수 있음을 증명하였다.

• 한국지반환경공학회 논문집
• /
• 제10권4호
• /
• pp.65-71
• /
• 2009

수압파쇄기술은 가스나 석유, 지열 등 자원추출을 하기 위해 다양한 분야에서 전세계적으로 응용되고 있는 기술이다. 이러한 수압파쇄 작업 시 복수의 균열이 필수적으로 발생하여 균열간 기계적인 상호작용을 유발하는데 이러한 상호작용은 수압파쇄시 얻어질 수 있는 결과(균열 폭, 균열 길이, 보어홀 내 압력)에 큰 영향을 끼치게 된다. 수치해석기법인 경계병치법은 이러한 균열간의 역학적 상호작용을 고려하는데 유효한 수치해석적 기법으로 개발이 되고 있으나 응력확대계수를 계산하는 해석식과의 비교 등을 통한 검증이 필요하다. 이를 위해 무한평면에 일축 인장 응력과 전단응력이 작용하는 단일균열의 경우 및 임의의 두 균열이 존재하는 경우의 응력확대계수 및 균열폭 해석식과 본 수치해석기법을 통해 얻은 값을 비교하였다. 그 결과, 본 연구에서 제시한 경계병치법은 해석식과 상당히 근접한 결과를 나타내어, 균열간의 기계적인 상호작용을 고려하는데 유효함을 검증하였으며, 추후 수압파쇄 시 설계에 필요한 균열폭 등의 변수를 계산하는데 사용할 수 있음을 나타내었다.

• 대한전기학회논문지
• /
• 제34권10호
• /
• pp.379-383
• /
• 1985

A method employing infinite elements is described for the magnetic field computations of the magnetic circuits with permanent magnet. The system stiffness matrix is derived by a variational approach, while the interfacial boundary conditions between the finite element regions and the infinite element regions are dealt with using collocation method. The proposed method is applied to a simple linear problems, and the numerical results are compared with those of the standard finite element method and the analytic solutions. It is observed that the proposed method gives more accurate results than those of the standard finite element method under the same computing efforts.

• Journal of Information Processing Systems
• /
• 제19권5호
• /
• pp.563-575
• /
• 2023

Trajectory planning is a key technology for unmanned aerial vehicles (UAVs) to achieve complex flight missions. In this paper, a terminal constraints conversion-based Gauss pseudospectral trajectory planning optimization method is proposed. Firstly, the UAV trajectory planning mathematical model is established with considering the boundary conditions and dynamic constraints of UAV. Then, a terminal constraint handling strategy is presented to tackle terminal constraints by introducing new penalty parameters so as to improve the performance index. Combined with Gauss-Legendre collocation discretization, the improved Gauss pseudospectral method is given in detail. Finally, simulation tests are carried out on a four-quadrotor UAV model with different terminal constraints to verify the performance of the proposed method. Test studies indicate that the proposed method performances well in handling complex terminal constraints and the improvements are efficient to obtain better performance indexes when compared with the traditional Gauss pseudospectral method.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2009년 춘계학술대회논문집
• /
• pp.239-244
• /
• 2009

The gridless (or meshfree) methods, such as MPS, SPH, FPM an so forth, are feasible and robust for the problems with moving boundary and/or complicated boundary shapes, because these methods do not need to generate a grid system. In this study, a gridless solver, which is based on the combination of moving least square interpolations on a cloud of points with point collocation for evaluating the derivatives of governing equations, is presented for two-dimensional unsteady incompressible Navier-Stokes problem in the low Reynolds number. A MAC-type algorithm was adopted and the Poission equation for the pressure was solved by successively in the moving least square sense. Some weighing functions were tested in order to investigate the up-winding effect for the convection term. Some typical problems were solved by the presented solver for the validation and the results obtained were compared with analytic solutions and the numerical results by conventional CFD methods, such as FVM.

• 대한수학회지
• /
• 제50권6호
• /
• pp.1291-1310
• /
• 2013

This paper develops least-squares pseudo-spectral collocation methods for elliptic boundary value problems having interface conditions given by discontinuous coefficients and singular source term. From the discontinuities of coefficients and singular source term, we derive the interface conditions and then we impose such interface conditions to solution spaces. We define two types of discrete least-squares functionals summing discontinuous spectral norms of the residual equations over two sub-domains. In this paper, we show that the homogeneous least-squares functionals are equivalent to appropriate product norms and the proposed methods have the spectral convergence. Finally, we present some numerical results to provide evidences for analysis and spectral convergence of the proposed methods.

• Structural Engineering and Mechanics
• /
• 제66권6호
• /
• pp.737-748
• /
• 2018

The current study presents a new technique in the framework of the nonlocal elasticity theory for a comprehensive buckling analysis of Euler-Bernoulli nano-beams made up of bidirectional functionally graded material (BDFGM). The mechanical properties are considered by exponential and arbitrary variations for axial and transverse directions, respectively. The various circumstances including tapering, resting on two-parameter elastic foundation, step-wise or continuous variations of axial loading, various shapes of sections with various distribution laws of mechanical properties and various boundary conditions like the multi-span beams are taken into account. As far as we know, for the first time in the current work, the buckling analyses of BDFGM nano-beams are carried out under mentioned circumstances. The critical buckling loads and mode shapes are calculated by using energy method and a new technique based on calculus of variations and collocation method. Fast convergence and excellent agreement with the known data in literature, wherever possible, presents the efficiency of proposed technique. The effects of boundary conditions, material and taper constants, foundation moduli, variable axial compression and small-scale of nano-beam on the buckling loads and mode shapes are investigated. Moreover the analytical solutions, for the simpler cases are provided in appendices.

• Structural Engineering and Mechanics
• /
• 제69권6호
• /
• pp.667-676
• /
• 2019

Minimizing the stress concentration around hypotrochoid hole in finite metallic plates under in-plane loading is an important consideration in engineering design. In the analysis of finite metallic plate, the effective factors on stress distribution around holes include curvature radius of the corner of the hole, hole orientation, plate's aspect ratio, and hole size. This paper aims to investigate the impact of these factors on stress analysis of finite metallic plate with central hypotrochoid hole. To obtain the lowest value of stress around a hypotrochoid hole, a swarm intelligence optimization method named ant lion optimizer is used. In this study, with the hypothesis of plane stress circumstances, analytical solution of Muskhelishvili's complex variable method and conformal mapping is employed. The plate is taken into account to be finite, isotropic and linearly elastic. By applying suitable boundary conditions and least square boundary collocation technique, undefined coefficients of stress function are found. The results revealed that by choosing the above-mentioned factor correctly, the lowest value of stress would be obtained around the hole allowing to an increment in load-bearing capacity of the structure.