• 한국소음진동공학회논문집
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• 제14권4호
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• pp.336-343
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• 2004

This paper reports the first known free vibration data for thin rectangular plates with V-notches. The classical Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. These sets include (1) mathematically complete algebraic-trigonometric polynomials which guarantee convergence to exact frequencies as sufficient terms are retained, and (2) corner functions which account for the bending moment singularities at the sharp reentrant corner of the Y-notch. Extensive convergence studies summarized herein confirm that the corner functions substantially enhance the convergence and accuracy of nondirectional frequencies for rectangular plates having the V-notch. In this paper, accurate frequencies and normalized contours of vibratory transverse displacement are presented for various notched plates, so that the effect of corner stress singularities may be understood.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 봄 학술발표회 논문집
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• pp.35-42
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• 2003

This paper provides the first known flexural vibration data for thick (Mindlin) rectangular plates having V-notches. The V-notch has bending moment and shear force singularities at its sharp corner due to the transverse vibratory bending motion. Based upon Mindlin plate theory, in which transverse shear deformation and rotary inertia effects are considered, the Ritz procedure is employed with a hybrid set of admissible functions assumed for the rotational and transverse vibratory displacements. This set includes: (1) a mathematically complete set of admissible algebraic-trigonometric polynomials which guarantee convergence to exact frequencies as sufficient terms are retained; and (2) an admissible set of Mindlin corner functions which account for the bending moment and shear force singularities at the sharp corner of the V-notch. Extensive convergence studies demonstrate the necessity of adding the Mindlin corner functions to achieve accurate frequencies for rectangular plates having sharp V-notches.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1998년도 가을 학술발표논문집(II)
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• pp.412-417
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• 1998

This paper provides accurate flexural vibration solutions for thick (Mindlin) sectorial plates. A Ritz method is employed which incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of Mindlin “corner functions". These corner functions model the singular vibratory moments and shear forces, which simultaneously exist at the vertex of corner angle exceeding 180$^{\circ}$. The first set guarantees convergence to the exact frequencies as sufficient terms are taken. The second set represents the corner singularities, and accelerates convergence substantially. Numerical results are obtained for completely free sectorial plates. Accurate frequencies are presented for a wide spectrum of vertex angles (90$^{\circ}$, 180$^{\circ}$, 270$^{\circ}$, 300$^{\circ}$, 330$^{\circ}$, 350$^{\circ}$, 35 5$^{\circ}$,and 359$^{\circ}$)and thickness ratios.tios.

• East Asian mathematical journal
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• 제36권5호
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• pp.583-591
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• 2020

In [8, 9] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with corner singularities, compute the finite element solutions using standard Finite Element Methods and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. The error analysis was given in [5]. In their approaches, the singular functions and the extraction formula which give the stress intensity factor are the basic elements. In this paper we consider the biharmonic problems with the cramped and/or simply supported boundary conditions and get the singular functions and its duals and find properties of them, which are the cornerstones of the approaches of [8, 9, 10].

• 한국강구조학회 논문집
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• 제12권4호통권47호
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• pp.363-374
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• 2000

본 논문에서는 고정, 단순, 또는 자유 연단 조건의 세 가지의 다른 조합을 갖는 마름모꼴형 평판의 진동에 대한 엄밀한 해석방법을 제시하였다. 본 논문의 주된 관점은 마름모꼴형 평판 둔각모서리에서 형성되는 모멘트특이도를 엄밀히 고려하여 해석하는 것이다. 단 영역 Lagrangian 범함수의 정상조건이 Ritz방법을 이용하여 유도되었다. 진동수의 수렴에 대한 연구는 모서리함수가 수렴속도를 가속화하는 것을 보여주고 있다. 본 논문에서는 모서리 응력특이도의 영향이 이해될 수 있도록 상당히 큰 둔각모서리를 갖는 마름모꼴 형 평판에 대한 정확한 진동수와 수직진동변위의 전형적인 등고선을 제시하였다.

• 호남수학학술지
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• 제40권4호
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• pp.785-794
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• 2018

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous Dirichlet boundary condition with one corner singularity at the origin, and compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. This approach uses the polar coordinate and the cut-off function to control the singularity and the boundary condition. In this paper we consider Poisson equations with multiple singular points, which involves different cut-off functions which might overlaps together and shows the way of cording in FreeFEM++ to control the singular functions and cut-off functions with numerical experiments.

• 한국조경학회지
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• 제45권4호
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• pp.118-130
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• 2017

조경 설계 과정에는 설계안을 시각화하는 다양한 종류의 드로잉이 제작된다. 이 연구는 조경 드로잉의 특성과 역할을 부단히 탐구해 온 제임스 코너의 재현 이론과 실천의 전개 과정을 면밀히 검토한 논문이다. 코너는 1990년대 초반부터 발표된 이론적 저술에서 드로잉이라는 시각 이미지는 경관의 다감각적 특성을 온전하게 담아내기 힘들고, 따라서 조경 드로잉은 경관의 외양을 사실적으로 그려내는 방식, 즉 도구적 기능보다는 경관의 다감각적 특성을 대안적으로 보여주고, 설계 과정에서 아이디어를 생성하는 상상적 역할을 담당해야 한다고 하면서 새로운 시각화 테크닉의 실험을 주장했다. 코너의 재현 이론은 1990년대 중후반 설계 실천에 적용되면서 실천적 이론으로 진화했다. 코너는 생태학을 수용하고, 랜드스케이프 어바니즘이라는 실무 작업을 전개해가면서 드로잉의 도구적 역할에 다시 주목했다. 이전에 코너가 콜라주와 몽타주를 이용하여 상상적 역할을 수행하는 퍼스펙티브 뷰를 지지하는 경향이 있었다면, 1990년대 후반의 이론과 실무 작업에서는 도구적 기능을 수행하는 맵을 기반으로 하되, 이를 상상적으로 변형하는 맵핑 테크닉을 강조했다. 이와 같이 코너의 저작은 조경 분야의 본질을 파악하여 드로잉의 특성과 역할을 체계적으로 이론화했고, 나아가 이론과 실천의 상호작용을 보여주고 있다는 점에서 현대 조경 설계에도 여전히 귀감이 되고 있다.

• Nuclear Engineering and Technology
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• 제31권2호
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• pp.214-225
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• 1999

An accurate method is presented for flexural vibrations of sectorial plates having simply supported-free and free-free radial edges, when the circular edge is either clamped or simply supported. The classical Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. These sets consist of : (1) mathematically complete algebraic-trigonometric polynomials which gurantee convergence to exact frequencies as sufficient terms are retained, and (2) comer functions which account for the bending moment singularities at re-entrant comer of the radial edges having arbitrary edge conditions. Accurate (at least four significant figures) frequencies and normalized contours of the transverse vibratory displacement are presented for the spectra of corner angles [90$^{\circ}$, 180$^{\circ}$(semi-circular), 270$^{\circ}$, 300$^{\circ}$, 330$^{\circ}$, 350$^{\circ}$, 355$^{\circ}$, 360$^{\circ}$ (complete circular)] causing a re-entrant comer of the radial edges. Future solutions drawn from alternative numerical procedures and finite element techniques may be compared with these accurate results.

• 한국신재생에너지학회:학술대회논문집
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• 한국신재생에너지학회 2005년도 춘계학술대회
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• pp.534-537
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• 2005

Free Vibration Analysis using Non-dimensional Dynamic Influence Function (NDIF) is extended to arbitrarily shaped plates including polygonal plates. Since the corners of polygonal plates have indefinite normal directions and additional boundary conditions related to a twisting moment at a corner along with moment and shear force zero conditions, it is not easy to apply the NDIF method to polygonal plates wi th the free boundary condition. Moreover, owing to the fact that the local polar coordinate system, which has been introduced for free plates with smoothly varying edges, cannot be employed for the straight edges of the polygonal plates, a new coordinate system is required for the polygonal plates. These problems are solved by developing the new method of modifying a corner into a circular arc and setting the normal direction at the corner to an average value of normal direct ions of two edges adjacent to the corner. Some case studies for plates with various shapes show that the proposed method gives credible natural frequencies and mode shapes for various polygons that agree well with those by an exact method or FEM (ANSYS).

• 한국전자파학회논문지
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• 제10권3호
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• pp.340-350
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• 1999

본 논문에서는 코너 리플렉터 안테나 구조로부터 변형된 W형 리플렉터 안테나를 제안하고, 모멘트법을 이용하여 복사특성을 해석하였다. 해석결과로 W형 리플렉터 안테나의 다이폴 높이 h와 back edge 거리 d를 변화시켰을 때 복사특성인 이득, 전후방비, 빔폭, 복사패턴을 각각 나타냈다. 또한 W형 리플렉터 안테나와 동일한 크기의 side 반사판을 갖는 코너 리플렉터 안테나의 복사특성을 비교한 결과 W형 리플렉터 안테나가 코너 리플렉터 안테나에 비해 다소 높고, 전후방비가 큼을 알 수 있었다. W형 리플렉터 안테나를 실제 제작하고, 복사특성을 측정하여 계산결과와 비교하였으며, 측정결과는 계산결과에 거의 근접한 것으로 나타났다.