• 한국구조물진단유지관리공학회 논문집
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• 제22권5호
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• pp.13-22
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• 2018

이 연구는 이방성 평판의 휨 해석을 위한 지배방정식을 유도하고 다양한 경계조건을 갖는 평판의 정확한 풀이과정을 제시하였다. 이 해법은 삼각급수를 이용하여 미분 방정식을 대수학적 방정식으로 변환시키는 전통적인 Navier와 Levy의 방법을 따랐다. Levy의 방법을 이용해 해를 구하려면 평판의 마주보는 두 끝단이 단순지지단인 경우에만 가능하다. Navier의 방법은 사각평판의 네 끝단이 모두 단순지지단 이어야 한다. 본 연구는 Navier와 Levy해법이 갖는 경계조건 한계를 극복하였다. 이 해법은 평판 네 끝단의 경계조건이 단순지지단과 고정단의 어떤 조합이라도 적용될 수 있다. 하중조건도 분포하중, 부분하중 그리고 선하중에 대해 적용할 수 있다. 이 해법의 장점은 Navier와 Levy해법이 갖는 경계조건 한계를 극복하였을 뿐만 아니라 정확한 해를 구할 수 있다. 비대칭 경계조건을 갖는 이방성평판에 대하여 이 해법을 이용한 계산결과를 나타냈다. 또한 Navier해법과 Levy해법 그리고 Szilard의 계산결과와 비교를 보여주었는데 계산된 처짐량이 잘 일치한다.

• 대한수학회지
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• 제50권4호
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• pp.771-795
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• 2013

In this paper we consider the Navier-Stokes equations in the half space. Our aim is to construct a mild solution for initial data in $B^{-\alpha}_{{\infty},{\infty}}(\mathbb{R}^n_+)$, 0 < ${\alpha}$ < 1. To do this, we derive the estimate of the Stokes flow with singular initial data in $B^{-\alpha}_{{\infty},q}(\mathbb{R}^n_+)$, 0 < ${\alpha}$ < 1, 1 < $q{\leq}{\infty}$.

• 한국항해학회지
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• 제9권2호
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• pp.43-63
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• 1985

As a circular cylinder has a comparatively simple shape and becomes a basic problem for flows around other various shapes of bodies, the problem of two-dimensional viscous flow around the circular cylinder has been investigated, both theoretically and experimentally. But not a few problems are left unsolved. It is well known that the calculations are successfully made with the approximations of Stokes or Oseen for very low Reynolds numbers, but as Reynolds number is increased, Oseen's approximations as well as Stokes's ones become more and more remote from the exact solution of the Navier-Stokes equations. Therefore, in this paper, the authors transform the Navier-Stokes equations into the finite difference equations in the steady two-dimensional viscous flow at Reynolds number up to 45, and then solve the solution of the Navier-Stokes equations numerically. Also, the authors examine the accuracy of the solution by means of flow visualization with aluminum powder. The main results are as follows; (1) The critical Reynolds number at which twin vortices begin to form in the rear of the circular cylinder is found to be 6 in the experiment and 4 in the numerical solution. (2) As Reynolds number is increased, it is proved that the ratio of the length of the twin vortices to the diameter is grown almost linearly, both experimentally and numerically. (3) Separation angle is also increased according to reynolds number. But it is found that it would converge into 101.3 degrees, both experimentally and numerically.

• 한국전산유체공학회지
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• 제17권2호
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• pp.35-41
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• 2012

This paper presents incompressible Navier-Stokes solution algorithm for 2D Free-surface flow problems on the Cartesian mesh, which was implemented to run on Graphics Processing Units(GPU). The INS solver utilizes the variable arrangement on the Cartesian mesh, Finite Volume discretization along Constrained Interpolation Profile-Conservative Semi-Lagrangian(CIP-CSL). Solution procedure of incompressible Navier-Stokes equations for free-surface flow takes considerable amount of computation time and memory space even in modern multi-core computing architecture based on Central Processing Units(CPUs). By the recent development of computer architecture technology, Graphics Processing Unit(GPU)'s scientific computing performance outperforms that of CPU's. This paper focus on the utilization of GPU's high performance computing capability, and presents an efficient solution algorithm for free surface flow simulation. The performance of the GPU implementations with double precision accuracy is compared to that of the CPU code using an representative free-surface flow problem, namely. dam-break problem.

• Structural Engineering and Mechanics
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• 제38권5호
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• pp.593-618
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• 2011

This paper deals with the problem of the determination of the response of a viscoelastic Bernoulli-Navier beam, which is resting on an elastic medium. Assuming uniaxial bending, the displacement of the beam axis is governed by an integro-differential equation. The compatibility of the displacements between the beam and the elastic medium is imposed through an integral equation. In general and in particular in the case of a Boussinesq medium, the solution has to be pursued numerically. On the contrary, in the case of a Winkler's medium the compatibility equation becomes a linear finite relationship, which allows finding an original analytical solution of the problem for both hereditary and aging behavior of the beam. Some numerical examples complete the paper, in which a comparison is made between the hereditary and the aging model for the creep of the beam.

• 한국항공우주학회지
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• 제33권9호
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• pp.34-40
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• 2005

본 연구에서는 비정상 유동해석을 위한 CFD 코드의 개발을 위해 대각화 ADI 기법을 적용한 정상 해석기법과 내재적 이중시간 전진기법을 도입하였다. 정상상태 Navier-Stokes 방정식의 Jacobian 행렬은 비점성항에 대해서만 적용하였고 여기에 내재적 인공점성 연산자를 첨가하여 블록 5대각 행렬을 유도하였다. 시간단축을 위해 스칼라 5대각 행렬로 대체하였다. 가상시간에 대한 정상상태기법에 실시간에 대한 미분항이 포함된 새로운 잔류항을 정의하였다. 가상시간에 대해 수렴된 해로부터 실시간 해를 구하고 시간에 대해 적분을 수행하는 내재적 이중시간 전진기법을 이용한 비정상 Navier-Stokes 코드를 개발하였다. 이에 대한 검증으로 정지한 유체속에 진동하는 평판문제, 원기둥 후방의 주기적인 Karman 와류생성, 이중원호 익형주위의 충격파 진동문제등을 수치해석하여 이론치, 실험치, 타연구자의 계산결과와 비교, 분석하였다.

• 한국방재학회 논문집
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• 제7권5호
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• pp.47-60
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• 2007

본 논문에서는 전단변형률과 회전관성을 고려한 준적합 쉘 요소를 이용한 점진기능재료 판과 쉘의 고유진동수와 좌굴하중을 연구하였다. S 형상 함수를 이용한 세라믹과 금속의체적요소의 변화에 따른 점진기능재료 판과 쉘의 고유치 문제를 연구하였다. 점진기능재료 쉘 요소의 면내 강성, 휨 강성 및 전단 강성의 수식은 등질 요소보다 복잡한 재료의 성질들로 결합되어 있다. 유한요소의 수치적 결과를 검정하기 위해 1차 전단변형 이론에 의한 직사각형 판의 Wavier해를 제시하였다. 적층복합 구조 및 S 형상 점진기능재료 구조의 수치해석해는 Navier의 해로 검증하였으며, S 형상 점진기능재료 구조물의 다양한 예제를 제시하였다. 해석결과는 Navier의 이론해와 아주 잘 일치함을 알 수 있었다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
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• pp.63-65
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• 2003

General classes of boundary-pressure-driven flows of incompressible Newtonian fluids in three­dimensional (3D) channels and in 3D pipes with known steady laminar realizations are investigated respectively. The characteristic physical and geometrical quantities of the flows are subsumed in the kinetic Reynolds number Re and a parameter $\psi$, which involves the energetic ratio and the directions of the boundary-driven part and the pressure-driven part of the laminar flow. The solution of non-stationary dimension-free Navier-Stokes equations is sought in the form $\underline{u}=u_{L}+U,\;where\;u_{L}$ is the scaled laminar velocity and periodical conditions are prescribed for U in the unbounded directions. The objects of our numerical investigations are autonomous systems (S) of ordinary differential equations for the time-dependent coefficients of the spatial Stokes eigenfunction, where these systems (S) were received by application of the Galerkin-method to the dimension-free Navier-Stokes equations for u.

• Steel and Composite Structures
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• 제27권6호
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• pp.761-775
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• 2018

In the present work, the recently developed non-polynomial shear deformation theories are assessed for thermo-mechanical response characteristics of laminated composite plates. The applicability and accuracy of these theories for static, buckling and free vibration responses were ascertained in the recent past by several authors. However, the assessment of these theories for thermo-mechanical analysis of the laminated composite structures is still to be ascertained. The response characteristics are investigated in linear and non-linear thermal gradient and also in the presence and absence of mechanical transverse loads. The laminated composite plates are modelled using recently developed six shear deformation theories involving different shear strain functions. The principle of virtual work is used to develop the governing system of equations. The Navier type closed form solution is adopted to yield the exact solution of the developed equation for simply supported cross ply laminated plates. The thermo-mechanical response characteristics due to these six different theories are obtained and compared with the existing results.

• Coupled systems mechanics
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• 제9권3호
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• pp.265-280
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• 2020

In this paper, a new refined hyperbolic shear deformation beam theory for the free vibration analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equations of motion are derived from the Hamilton's principle. Navier type solution method was used to obtain frequencies, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the free vibration response of a simply supported FG beams.