• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집E
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• pp.422-429
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• 2001

A two dimensional hierarchical elements are investigated for a use on the incompressible flow computation. The construction of hierarchical elements are explained through the tensor product of 1-D hierarchical functions, and a systematic treatment of essential boundary values has been developed for the degrees of freedom corresponding to higher order terms. The numerical study for the poisson problem showed that the present scheme can increase the convergence and accuracy of finite element solutions, and can be more efficient than the standard first order with many elements. Also, for Stokes and cavity flow cases, solutions from hierarchical elements showed better resolutions and future promises for higher order solutions.

• 전기의세계
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• 제23권3호
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• pp.43-52
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• 1974

The matrix inversion is very inefficient for computing direct solutions of the large spare systems of linear equations that arise in many network problems as a large electrical power system. Optimally ordered triangular factorization of sparse matrices is more efficient and offers the other important computational advantages in some applications with this method. The direct solutions are computed from sparse matrix factors instead of a full inverse matrix, thereby gaining a significant advantage is speed and computer memory requirements. In this paper, it is shown that the sparse matrix method is superior to the inverse matrix method to solve the linear equations of large sparse networks. In addition, it is shown that the sparse matrix method is superior to the inverse matrix method to solve the linear equations of large sparse networks. In addition, it is shown that the solutions may be applied directly to sove the load flow in an electrical power system. The result of this study should lead to many aplications including short circuit, transient stability, network reduction, reactive optimization and others.

• 한국전산유체공학회지
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• 제12권3호
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• pp.29-40
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• 2007

An implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes. The method can achieve high-order spatial accuracy by using hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. Also, the flows around a 2-D circular cylinder and an NACA0012 airfoil were numerically simulated. The numerical results showed that the implicit discontinuous Galerkin methods couples with a high-order representation of curved solid boundaries can be an efficient method to obtain very accurate numerical solutions on unstructured meshes.

• 한국전산유체공학회지
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• 제16권4호
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• pp.72-83
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• 2011

A high-order discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations was developed on unstructured triangular meshes. For this purpose, the BR2 methd(the second Bassi and Rebay discretization) was adopted for space discretization and an implicit Euler backward method was used for time integration. Numerical tests were conducted to estimate the convergence order of the numerical solutions of the Poiseuille flow for which analytic solutions are available for comparison. Also, the flows around a flat plate, a 2-D circular cylinder, and an NACA0012 airfoil were numerically simulated. The numerical results showed that the present implicit discontinuous Galerkin method is an efficient method to obtain very accurate numerical solutions of the compressible Navier-Stokes equations on unstructured meshes.

• Management Science and Financial Engineering
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• 제16권3호
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• pp.71-84
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• 2010

In this study, we present the exact methods of transforming the continuous solutions into the discrete ones for two types of bit-loading problem, marginal adaptive (MA) and rate adaptive (RA) problem, in multicarrier communication systems. While the computational complexity of existing solution methods for discrete optimal solutions depends on the number of bits to be assigned (R), the proposed method determined by the number of subcarriers (N), making ours be more efficient in most cases where R is much larger than N. Furthermore our methods have some strength of their simpler form to make a practical use.

• Advances in materials Research
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• 제8권4호
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• pp.313-335
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• 2019

The objective of the present paper is to investigate the bending and free vibration behavior of functionally graded material (FGM) sandwich rectangular plates using an efficient and simple higher order shear deformation theory. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The most interesting feature of this theory is that it does not require the shear correction factor. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Earthquakes and Structures
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• 제19권2호
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• pp.91-101
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• 2020

This work presents an efficient and original hyperbolic shear deformation theory for the bending and dynamic behavior of functionally graded (FG) beams resting on Winkler - Pasternak foundations. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present theory, the equations of motion are derived from Hamilton's principle. Navier type analytical solutions are obtained for the bending and vibration problems. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and vibration behavior of functionally graded beams.

• Structural Engineering and Mechanics
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• 제12권1호
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• pp.85-100
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• 2001

In this paper, an analytical procedure for solving several static and dynamic problems of non-uniform beams is proposed. It is shown that the governing differential equations for several stability, free vibration and static problems of non-uniform beams can be written in the from of a unified self-conjugate differential equation of the second-order. There are two functions in the unified equation, unlike most previous researches dealing with this problem, one of the functions is selected as an arbitrary expression in this paper, while the other one is expressed as a functional relation with the arbitrary function. Using appropriate functional transformation, the self-conjugate equation is reduced to Bessel's equation or to other solvable ordinary differential equations for several cases that are important in engineering practice. Thus, classes of exact solutions of the self-conjugate equation for several static and dynamic problems are derived. Numerical examples demonstrate that the results calculated by the proposed method and solutions are in good agreement with the corresponding experimental data, and the proposed procedure is a simple, efficient and exact method.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1995년도 추계학술대회 논문집 학회본부
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• pp.89-91
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• 1995

This paper describes an extension or a pair or multiple load flow solutions and nose curve method developed for voltage stability analysis or AC power systems to AC/DC systems. In this approach the converters are regarded as voltage dependent loads. Assuming that the converters at the unstable (-mode) solution consume the same power equal to the power at the stable (+mode) solution, the unstable solutions or the nose curves arc determined. This method is very efficient since estimating voltage collapse point and voltage stability margin arc determined by a few iterations of multiple load flow solutions. Also the method has the advantages that since the structure or Jacobian matrix is same with that of AC load flow, modal analysis or voltage stability is readily applicable if desired.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2007년도 춘계 학술대회논문집
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• pp.30-40
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• 2007

The implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes, which can achieve higher-order accuracy by wing hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. And, the flows around a circle and a NACA0012 airfoil was also numerically simulated. Numerical results show that the implicit discontinuous Galerkin methods with higher-order representation of curved solid boundaries can be an efficient higher-order method to obtain very accurate numerical solutions on unstructured meshes.