• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권2호
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• pp.99-106
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• 2005

We present a relation between the orthogonality of the constrained Legendre polynomials over the triangular domain and the BB ($B{\acute{e}zier}\;-Bernstein$) coefficients of the polynomials using the equivalence of orthogonal complements. Using it we also show that the best constrained degree reduction of polynomials in BB form equals the best approximation of weighted Euclidean norm of coefficients of given polynomial in BB form from the coefficients of polynomials of lower degree in BB form.

• Current Applied Physics
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• 제18권11호
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• pp.1327-1337
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• 2018

This paper investigates the vibration behavior of pristine and defected triangular graphene sheets; which has recently attracted the attention of researchers and compare these two types in natural frequencies and sensitivity. Here, the molecular dynamics method has been employed to establish a virtual laboratory for this purpose. After measuring the different parameters obtained by the molecular dynamics approach, these data have been analyzed by using the frequency domain decomposition (FDD) method, and the dominant frequencies and mode shapes of the system have been extracted. By analyzing the vibration behaviors of pristine triangular graphene sheets in four cases (right angle of 45-90-45 configuration, right angle of 60-90-30 configuration, equilateral triangle and isosceles triangle), it has been demonstrated that the natural frequencies of these sheets are higher than the natural frequency of a square sheet, with the same number of atoms, by a minimum of 7.6% and maximum of 26.6%. Therefore, for increasing the resonance range of sensors based on 2D materials, nonrectangular structures, and especially the triangular structure, can be considered as viable candidates. Although the pristine and defective equilateral triangular sheets have the highest values of resonance, the sensitivity of defective (45,90,45) triangular sheet is more than other configurations and then, defective (45,90,45) sheet is the worst choice for sensor applications.

• 대한전기학회논문지
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• 제35권11호
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• pp.479-486
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• 1986

It is necessary to consider a rotor movement in dynamic analysis on the flux distribution of electric machinery by FEM. Therefore, if air-gap domain was subdivided into triangular elements, computation results contain errors due to variation of element shape in air-gap because the nodal points corresponding to the rotor are displaced in analyzing domain for the time difference. In order to reduce this errors, the paper presents a application of a Macro Air-gap Element that interpolation function is obtained analytically and a means to join it with linear triangular elements in the rotating machine or in the linear machine. At the end of paper, setting up analytic domain model, it compares analytic solution with the computation results of Macro Air-gap Element appliction and that of linear triangular element subdivision only to each cases of nodal displacement. And it carries out that errors due to variation of element shape are reduced effectively by application of a Macro air-gap element.

• 대한기계학회논문집A
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• 제24권1호
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• pp.240-249
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• 2000

An improved global optimization algorithm is developed by extending the domain elimination method. The concept of triangular patch consists of two or more trajectories of local minimizations is introduced to widen the attraction region of the domain elimination method. Using the an-]c between each of three vertices of the patch and a design point, we measure the proximity, between the design point and the patch. With the Gram-Schimidt orthonormalization, this method can be extended to general n-dimensional problems. We code the original domain elimination algorithm and a patch-based algorithm. Then we compare the performance of two algorithms. Through the well-known example problems. the algorithm using patch is shown to be superior to the original domain elimination algorithm in view of computational efficiency.

• 한국CDE학회논문집
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• 제4권2호
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• pp.79-86
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• 1999

A general approach to automatic generation of triangular meshes on three-dimensional surfaces is presented in this paper. The approach, developed with emphasis on program generality and interface with CAD/CAM systems, is based on the double mapping method and the looping method. The double mapping method is introduced and anew splitting scheme is proposed for the looping method employed for triangular mesh generation on the parametric domain. Several application examples are given.

• 한국항공우주학회지
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• 제32권9호
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• pp.41-48
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• 2004

본 논문에서는 빠른 요소망 자료 처리를 위해 영역기반 해쉬구조를 개발하고 이에 기반한 효율적 삼각형 자동 요소망 생성 알고리듬을 제안하였다. 제안된 알고리듬에서는 신속하게 최적의 절점을 생성하고 삼각형 생성시 예외처리를 줄일 수 있도록 Advancing layer method 와 Delaunay 삼각화 방법이 함께 이용되었다. 본 알고리듬의 성능을 검증하기 위하여 개발된 2차원 자동 요소망 생성 프로그램을 이용하여 볼록한 모델, 오목한 모델 및 복잡한 형태의 모델에 대한 요소망 생성 테스트를 수행하고, 그 성능을 상용 소프트웨어와 비교하였다.

• 한국CDE학회논문집
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• 제1권1호
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• pp.56-64
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• 1996

A quadrilateral-triangular mixed grid method for the solution of incompressible viscous flow is presented. The solution domain near the body surface is meshed using elliptic grid geneator to acculately simulate the viscous flow. On the other hand, we used unstructured triangular grid system generated by advancing front technique of a simple automatic grid generation algorithm in the rest of the computational domain. The present method thus is capable of not only handling complex geometries but providing accurate solutions near body surface. The numerical technique adopted here is PISO type finite element method which was developed by the present author. Investigations have been made of two-dimensional unsteady flow of Re=550 past a circular cylinder. In the case of use of the unstructured grid only, there exists a considerable amount of difference with the existing results in drag coefficient and vorticity at the cylinder surface; this may be because of the lack of the grid clustering to the surface that is a inevitable requirement to resolve the viscous flow. However, numerical results on the mixed grid show good agreements with the earlier computations and experimental data.

• 한국CDE학회논문집
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• 제1권3호
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• pp.224-233
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• 1996

An automatic mesh generation scheme with triangular finite elements on three-dimensional surfaces has been developed. The surface triangulation process is performed as follows. To begin, surfaces with key nodes are transformed to two-dimensional planes and the meshes with triangular elements are constructed in these planes. Finally, the constructed meshes are transformed back to the original 3D surfaces. For the mesh generation, an irregular mesh generation scheme is employed in which local mesh densities are assigned by the user along the boundaries of the analysis domain. For this purpose a looping algorithm combined with an advancing front technique using basic operators has been developed, in which the loops are recursively subdivided into subloops with the use of the best split lines and then the basic operators generate elements. Using the split lines, the original boundaries are split recursively until each loop contains a certain number of key nodes, and then using the basic operators such as type-1 and type-2, one or two triangular elements are generated at each operation. After the triangulation process has been completed for each meshing domain, the resulting meshes are finally improved by smoothing process. Sample meshes are presented to demonstrate the versatility of the algorithm.

• Journal of the Optical Society of Korea
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• 제15권2호
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• pp.118-123
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• 2011

A novel triangular-shaped plasmonic metal-insulator-metal (MIM) Bragg grating waveguide is introduced, whose band-gap is narrower than that of the conventional step type and wider than that of the sawtoothshaped one. Moreover apodized triangular-shaped MIM Bragg grating structures are proposed in order to reduce the side lobes of the transmission spectrum, because the Bragg reflector with a sawtooth profile has a smoother transmission spectrum than that of a triangular-shaped one. The performance of the proposed structures is simulated by using the finite difference time domain method.

• 한국게임학회 논문지
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• 제2권1호
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• pp.62-68
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• 2002

본 연구에서는 기존의 곡면 삼각화 방법들이 많은 수의 삼각형 메쉬를 사용하면서도 정확하게 표현하기가 힘들었던, 날카로운 모서리를 가지는 곡면을 처리할 수 있는 trammed NURBS곡면 삼각화 방법을 제안, 구현하였다. 기존의 매개변수영역에서의 삼각화의 문제점인 3차원공간상의 삼각형 메쉬를 계산할 때의 왜곡현상을 해결하기 위해서 곡면의 펼친영역을 근사적으로 계산하여 삼각화 하는 방법을 사용했다. 곡선, 곡면의 날카로운 점과 모서리를 자동으로 인식하기 위해서 1차미분 연속조건을 이용하였고, 이를 제약조건으로 constraint Delaunay 삼각화방법을 사용하여 곡면의 날카로운 형상(sharp shape)을 유지하면서 삼각화를 수행할 수 있었다. 제안된 삼각화 방법은 기존의 삼각화 방법에 비하여 적은수의 삼각형 메쉬로 곡면의 날카로운 모서리를 보다 정확하게 표현 할 수 있는 장점을 가지고 있어서 삼각형의 개수에 따라 가시화 성능이 큰 영향을 받는 컴퓨터게임 같은 분야에 도움을 줄 수 있으리라 예상된다.