• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집B
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• pp.590-595
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• 2001

To improve the modeling accuracy for the finite element method, this paper proposes a method to make a combined use of finite elements and exact dynamic elements. Exact interpolation functions for a Timoshenko beam element are derived and compared with interpolation functions of the finite element method (FEM). The exact interpolation functions are tested with the Laplace variable varied. The exact interpolation functions are used to gain more accurate mode shape functions for the finite element method. This paper also presents a combined use of finite elements and exact dynamic elements in design problems. A Timoshenko frame with tapered sections is tested to demonstrate the design procedure with the proposed method.

• 한국강구조학회 논문집
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• 제13권6호
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• pp.703-713
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• 2001

비대칭단면을 갖는 박벽 직선보의 3차원 자유진동해석을 수행하기 위하여 엄밀한 요소강도행렬을 유도한다. 단면이 균일한 비대칭 박벽 탄성보에 대하여 운동방정식, 힘-변위 관계식을 유도하고 엄밀한 동적강도행렬을 수치적으로 산정하는 방법을 제시한다. 14개의 변위파라미터를 도입하여 고차의 연립미분방정식을 1차 연립미분방정식으로 바꾸고, 비대칭행렬을 갖는 선형 고유치문제의 해를 복소수영역에서 구한다. 이를 이용하여 절점변위에 대한 처짐함수을 엄밀히 구하고, 재단력-변위 관계식을 이용하여 엄밀한 동적요소강도행렬을 산정한다. 본 방법의 타당성을 보이기 위하여 비대칭 박벽보의 고유진동수를 계산하고, 해석해, 혹은 3차 Hermitian 다항식을 사용한 보요소 및 ABAQUS를 사용한 유한요소 해석결과와 비교한다.

• 한국전산구조공학회논문집
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• 제15권3호
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• pp.463-469
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• 2002

탄성지반 위에 놓인 보-기둥 요소의 총포텐셜 에너지로부터 변분원리를 적용하여 지배방정식과 힘-변위 관계식을 유도하였다. 4계 상미분방정식 형태의 지배방정식을 4개의 변위 파라메타를 도입하여 1계 연립미분방정식 형태의 선형 고유치 문제로 전환하고, 힘-변위 관계식을 적용하여 엄밀한 정적, 동적 요소강성행렬을 유도하였다. 직접강성법을 이용하여 구조물 강성행렬을 구하고, 2차원 보-기둥구조의 엄밀한 좌굴하중과 고유진동수를 구하고, 결과를 유한요소해와 비교함으로써 본 연구의 타당성을 검증하였다. 이러한 엄밀한 해석방법은 Hermitian 다항식을 형상함수로 도입하여 요소의 강성행렬을 산정하는 유한요소법과 비교할 때, 요소의 수를 대폭 줄일 수 있는 장점이 있다.

• 한국정밀공학회지
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• 제18권8호
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• pp.87-95
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• 2001

Although asymmetric beams are widely used in industry, few research results are available on the dynamic modeling and analysis of structure including asymmetric beams. Asymmetric beams cause complicated vibration phenomena due to the inherent bending-torsion coupled vibration. In this paper, an exact dynamic element matrix for the bending-torsion coupled vibration of asymmetric beam is derived. The application of the derived exact dynamic element matrix is demonstrated by some illustrative examples wherein the natural frequencies by the proposed modeling method are compared with those available in the literature. Another numerical example is also illustrated which deals with a general beam with joints. The numerical study shows that the exact dynamic element model is useful for the dynamic analysis of asymmetric bending-torsion coupled beams.

• 소음진동
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• 제9권5호
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• pp.966-974
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• 1999

This paper introduces modeling and its modal analysis procedure for exact and closed form solution of in-plane vibrations of general Timoshenko frame structures using exact dynamic element method(EDEM). The derivation procedure of the exact system dynamic matrices for Timoshenko beam frames is described. A new modal analysis procedure is also proposed since the conventional modal analysis schemes are not adequate for the proposed, exact system dynamic matrix. The proposed method provides exact modal parameters as well as all kinds of closed form solutions for general frame structures. Two numerical examples are presented for validating and illustrating the proposed method. The numerical study proves that the proposed method is useful for dynamic analysis of frame structures.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 추계학술대회논문집
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• pp.540-545
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• 2000

This paper presents the exact dynamic element for composite Timoshenko beam, which is inherently subject both to bending and torsional vibration. The coupling effect between bending and torsional vibrations is rigorouly considered in the derivation of the exact dynamic element. Two examples are provided to validate and illustrate the proposed exact dynamic element matrix for composite Timoshenko beam.

• 한국소음진동공학회논문집
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• 제12권2호
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• pp.141-149
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• 2002

Although the finite element method has become an indispensible tool for the dynamic analysis of structures, difficulty remains to quantify the errors associated with discretization. To improve the modeling accuracy, this paper proposes a method to make a combined use of finite elements and exact dynamic elements. Exact interpolation functions for the Timoshenko beam element are derived using the exact dynamic element modeling (EDEM) and compared with interpolation functions of the finite element method (FEM). The exact interpolation functions are tested with the Laplace variable varied. A combined use of finite element method and exact interpolation functions is presented to gain more accurate mode shape functions. This paper also presents a combined use of finite elements and exact dynamic elements in design/reanalysis problems. Timoshenko flames with tapered sections are tested to demonstrate the design procedure with the proposed method. The numerical study shows that the combined use of finite element model and exact dynamic element model is very useful.

• 한국강구조학회 논문집
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• 제14권4호
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• pp.509-518
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• 2002

비대칭 단면을 갖는 박벽보의 3차원 휨-배틂 좌굴해석 및 정적해석을 위하여, 평형방정식과 힘-변위 관계식을 이용하여 엄밀한 정적요소강성행렬을 수치적으로 산정하는 개선된 기법을 제시한다. 먼저 14개의 변위피라미터를 도입하여 고차의 연립미분방정식을 1차 연립미분방정식으로 변환하고, 복소수 영역에서 선형고유치문제를 해를 구한다. 이 경우 동적강성행렬을 산정하는 경우와는 달리 복수개의 '영'의 고유치가 발생한다. 이에 대응하는 변위피라미터의 다항식을 항등식 조거능로부터 구하고, 이를 고유치와 결합하여 박벽보 요소의 엄밀한 처짐함수를 구한다. 이렇게 구한 엄밀한 처짐함수에 재단력-변위 관계식을 적용하여 세가지 초기단면력 조건에 대응하는 엄밀한 정적요소강성행렬을 산정한다. 본 방법의 타당성을 보이기 위하여 비대칭 박벽보의 좌굴하중과 처짐값을 계산하고 해석해나 ABAQUS 쉘요소를 이용한 해석결과 및 직선보요소를 사용한 유한요소해의 결과와 비교, 검증한다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1997년도 추계학술대회 논문집
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• pp.609-612
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• 1997

This paper deals with in-plane vibration analysis of curved beams. The exact dynamic element method is applied to obtain the dynamic model for curved beams. Numerical examples are provided to validate the proposed modeling and analysis method. The numerical results show that the proposed method is useful for the dynamic analysis of curved beams.

• 한국정밀공학회지
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• 제20권6호
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• pp.197-204
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• 2003

This paper presents an efficient modeling and dynamic analysis method for open cracked beam structures. An equivalent bending spring model is introduced to represent the structural weakening effect in the presence of cracks. The proposed method adopts the exact dynamic element method (EDEM) to avoid the inconvenience and numerical errors in association with re-meshing the structural model with the crack position changed. The proposed modeling method is validated through a series of simulation and experiments. First, the proposed method is rigorously compared with a commercial finite element code. Then, two kinds of experiments are performed to validate the proposed modeling method. Finally, a diagnostic scheme fur open cracked beam structures is proposed and demonstrated through a numerical example.