• 한국전산유체공학회지
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• 제9권3호
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• pp.8-17
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• 2004

A Semi-Lagrangian method based on CIP(Cubic Interpolated Pseudoparticle)method is proposed and it is applied to solve the two dimensional advection equation. Especially the attentions are given to settle the pole problem and to enhance the accuracy in solving the advection equation on the spherical coordinate system. Tn this algorithm, the CU method is employed as the Semi-Lagrangian method and extended to the spherical coordinate system. To enhance the accuracy of the solution, the spatial discretization is made by CIP method. The mathematical formulation and numerical results are also described. To verify the efficiency, accuracy and capability of proposed algorithm, two dimensional rotating cosine bell problem and the frontogenesis problem are simulated by the present scheme. As results, it is confirmed that the present scheme gives an accurate solution and settles the pole problem in the advection equation on the sphere.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권4호
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• pp.389-389
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• 2016

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.415-426
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• 2020

In this paper, we will prove some uniqueness theorems that can be applied to the generalized Hyers-Ulam stability of some additive-quadratic-cubic functional equation in complete modular spaces without Δ₂-conditions.

• 한국산학기술학회논문지
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• 제22권6호
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• pp.19-26
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• 2021

격자 구조체는 강도 및 강성, 초경량 및 에너지 흡수 능력 등의 우수성을 가지고 있어서 전방위 산업에서 주목을 받고 있으나, 다양한 장점에도 불구하고 복잡한 형상에 따른 제조 공정의 어려움으로, 현재까지 광범위한 상용화 및 사용은 제한되고 있다. 한편 적층 제조는 전통적인 제조 방법으로는 불가능한 복잡한 기하학적 형상 제조가 가능한 기술로써, 격자 구조체 제조를 위한 최적 기술로 주목을 받고 있다. 본 연구에서는 3차원 좌표 방법으로 단위 셀을 형성하고, 단위셀의 바운더리 박스 크기 및 스트럿 반경에 따른 상대 밀도의 관계식을 도출하였다. 본 연구에서는 Simple Cubic(SC), Body-Centered Cubic(BCC) 및 Face-Centered Cubic(FCC)을 모델링 소프트웨어를 사용하여 상대 밀도 맞춤형 구조체를 설계하였다. 본 연구에서 제안한 상대 밀도 산출식 정확도는 SC, BCC 및 FCC에서 98.3 %, 98.6 % 및 96.2%의 신뢰성을 확보하였다. 격자 구조체를 대상으로 시뮬레이션 수행 결과, 동일한 셀 배열 조건에서는 상대 밀도가 커짐에 따라 항복 하중이 커지고, 동일 배열 조건에서는 SC, BCC, FCC 순으로 압축 항복 하중이 작아지는 결과가 나타났다. 최종적으로 20 mm × 20 mm × 20 mm 크기의 구조체는 SC 단위 셀을 3×3×3 배열로 구성하는 것이 압축 하중에 대한 구조적 최적화가 가능한 것으로 나타났다.

• 한국건축시공학회지
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• 제6권1호
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• pp.101-107
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• 2006

While a Study with regard to the measurement on Concrete Strength and the Change of Drying Shrinkage in accordace with Content Ratio of Crushed Stone Powder, it is being analyzed as the result that the strength according to Content Ratio of crushed Stone Powder is somewhat lowering. Accordingly, it is the real situation that the Concrete mixed with Crushed Stone Powder is utilized for non-structural material, not for the structural material. Therefore, this Research willing to furnish the suitable utilizing scheme for construction site as well as practical life by means of conduct the experiment on both Concrete Pressure Strength according to mixture with Crushed Stone Powder and Elastic Modulus, it also presumes the optimum Elastic Modulus Equation after analysis of comparison with common concrete strength. As the result of the experiment, in case of the Content Ratio of Crushed Stone Powder is less than 5%, it did not display a big difference in its both strength and matter-property compare with common concrete. In case of Elastic Modulus, when the Pressure Strength is 50% and 40% respectively, the Elastic Modulus Equation accords very well with the provided condition of Quadratic function, and as the result of the Presumption on Elastic Modulus according to Content of Crushed Stone Powder, in case the Pressure Strength is 50%, Elastic Modulus Equation showed that Error Ratio of Cubic function is at degree of 0.0005%, in case the Pressure Strength is 40%, Elastic Modulus Equation was accorded well with the value of the experimental data likely as the Error Ratio of Cubic function is at the degree around 0.0034%, respectively.

• Structural Engineering and Mechanics
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• 제38권2호
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• pp.211-229
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• 2011

In this paper, we present a new explicit procedure using periodic cubic B-spline interpolation polynomials to solve linear and nonlinear dynamic equation of motion governing single degree of freedom (SDOF) systems. In the proposed approach, a straightforward formulation was derived from the approximation of displacement with B-spline basis in a fluent manner. In this way, there is no need to use a special pre-starting procedure to commence solving the problem. Actually, this method lies in the case of conditionally stable methods. A simple step-by-step algorithm is implemented and presented to calculate dynamic response of SDOF systems. The validity and effectiveness of the proposed method is demonstrated with four examples. The results were compared with those from the numerical methods such as Duhamel integration, Linear Acceleration and also Exact method. The comparison shows that the proposed method is a fast and simple procedure with trivial computational effort and acceptable accuracy exactly like the Linear Acceleration method. But its power point is that its time consumption is notably less than the Linear Acceleration method especially in the nonlinear analysis.

• Geomechanics and Engineering
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• 제22권5호
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• pp.375-384
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• 2020

In this study, the application of conventional cubic law to a deep depth condition was experimentally evaluated. Moreover, a modified equation for estimating the rock permeability at a deep depth was suggested using precise hydraulic tests and an effect analysis according to the vertical stress, pore water pressure and fracture roughness. The experimental apparatus which enabled the generation of high pore water pressure (< 10 MPa) and vertical stress (< 20 MPa) was manufactured, and the surface roughness of a cylindrical rock sample was quantitatively analyzed by means of 3D (three-dimensional) laser scanning. Experimental data of the injected pore water pressure and outflow rate obtained through the hydraulic test were applied to the cubic law equation, which was used to estimate the permeability of rock fracture. The rock permeability was estimated under various pressure (vertical stress and pore water pressure) and geometry (roughness) conditions. Finally, an empirical formula was proposed by considering nonlinear flow behavior; the formula can be applied to evaluations of changes of rock permeability levels in deep underground facility such as nuclear waste disposal repository with high vertical stress and pore water pressure levels.

• Structural Engineering and Mechanics
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• 제30권5호
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• pp.593-602
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• 2008

This paper presents a new linearization algorithm to find the periodic solutions of the Duffing equation, under harmonic loads. Since the Duffing equation models a single degree of freedom system with a cubic nonlinear term in the restoring force, finding its periodic solutions using classical harmonic balance (HB) approach requires numerical integration. The algorithm developed in this paper replaces the integrals appearing in the classical HB method with triangular matrices that are evaluated algebraically. The computational cost of using increased number of frequency components in the matrixbased linearization approach is much smaller than its integration-based counterpart. The algorithm is computationally efficient; it only takes a few iterations within the region of convergence. An example comparing the results of the linearization algorithm with the "exact" solutions from a 4th order Runge- Kutta method are presented. The accuracy and speed of the algorithm is compared to the classical HB method, and the limitations of the algorithm are discussed.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2011년도 제36회 춘계학술대회논문집
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• pp.89-92
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• 2011

초임계 압력 조건에서 분사된 액체추진제의 혼합 및 연소 현상을 해석하기 위해서는 열역학적 비이상성과 전달 물성치의 특이성을 예측하는 것이 선행되어야 한다. 본 연구에서는 일반화된 3차 상태방 정식(cubic EoS)을 기반으로 실제유체의 열역학/전달 물성치를 계산하는 서브루틴들을 개발하였으며, 표준 화학반응 패키지인 Chemkin과 쉽게 연동될 수 있도록 하였다. 실제유체 해석 패키지를 이용하여 기존의 층류화염편 코드를 확장하였으며, 실제 로켓엔진이 갖는 고압 연소조건하에서 케로신과 액체산소의 국소화염구조에 대한 수치해석 연구를 수행하였다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2009년 추계학술대회논문집
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• pp.49-55
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• 2009

This paper evaluates performances of a recently developed divergence-free finite element method based on Hermite interpolated stream functions. Velocity bases are derived from Hermite interpolated stream functions to form divergence-free basis functions. These velocity basis functions constitute a solenoidal function space, and the simple gradient of the Hermite functions constitute an irrotational function space. The incompressible Navier-Stokes equation is orthogonally decomposed into a solenoidal and an irrotational parts, and the decoupled Navier-Stokes equations are projected onto their corresponding spaces to form proper variational formulations. To access accuracy and convergence of the present algorithm, three test problems are selected. They are lid-driven cavity flow, flow over a backward-facing step and buoyancy-driven flow within a square enclosure. Hermite interpolation functions from cubic to quintic are chosen to run the test problems. Numerical results are shown. In all cases it has shown that the present method has performed well in accuracies and convergences. Moreover, the present method does not require an upwinding or a stabilized term.