NURBS 곡면기반의 기하학적 모델링과 셀 유한요소해석의 연동

최진복,노희열,조맹효,Choi, Jin-Bok,Roh, Hee-Yuel,Cho, Maeng-Hyo 대한기계학회 2007 大韓機械學會論文集A Vol.31 No.1

The linkage framework of geometric modeling based on NURBS(Non-Uniform Rational B-Spline) surface and shell finite analysis is developed in the present study. For this purpose, geometrically exact shell finite element is implemented. NURBS technology is employed to obtain the exact geometric quantities for the analysis. Especially, because NURBS is the most powerful and wide-spread method to represent general surfaces in the field of computer graphics and CAD(Computer Aided Design) industry, the direct computation of surface geometric quantities from the NURBS surface equation without approximation shows great potential for the integration between geometrically exact shell finite element and geometric modeling in the CAD systems. Some numerical examples are given to verify the performance and accuracy of the developed linkage framework. In additions, trimmed surfaces with some cutouts are considered for more practical applications.

NURBS 기반 캐드시스템의 곡면 모델링과 쉘 유한요소해석의 연동

최진복(Jin Bok Choi),노희열(Hee Yuel Rho),조맹효(Maenghyo Cho) 한국자동차공학회 2005 한국자동차공학회 Symposium Vol.- No.-

The linkage framework of surface geometric modeling and analysis based on the NURBS technology is developed in this study. The NURBS surfaces are generated by interpolating given set of data points or by extracting the necessary information to construct the NURBS surface from the IGES file which is generated by the commercial CAD systems in the present study. Some numerical examples that show the tendency of displacement convergence according to the paramterization method of the NURBS surface are given. And quadric shape surfaces which is generated exactly based on NURBS representation is considered. It is the one of the advantages of the NURBS equation to express quadric shape curves or surfaces exactly in the mathematical point of view. A trimmed surfaces which are often encountered during modeling process in the CAD systems are handled briefly in the present study.

NURBS 기반의 곡면 모델링과 쉘 유한요소해석의 연동

최진복(Jin Bok Choi),노희열(Hee Yuel Rho),조맹효(Maenghyo Cho) 대한기계학회 2006 대한기계학회 춘추학술대회 Vol.2006 No.11

In this study, we implement a framework that directly links a general tensor-based shell finite element to NURBS(Non-Uniform Rational B-Spline) geometric modeling. The quantities for the shell finite element analysis are calculated directly from the NURBS surface equations without any interpolation of nodal values, the geometry errors can be dramatically reduced. The NURBS surfaces can be easily generated by interpolating or approximating the given set of data points through SMLib in our study. Our developed framework can also import the surface data in IGES file format modeled in the commercial CAD systems and convert those surfaces into NURBS surfaces for the shell finite analysis. Our proposed framework can analyze more general type of surfaces such as trimmed or blended surfaces as well as complex shaped ones. That is, the integration of our linkage framework with the CAD surface modeling based on NURBS is accomplished successfully.

NURBS 기반 캐드시스템의 곡면 모델링과 쉘 유한요소해석의 연동

최진복(Jin Bok Choi),노희열(Hee Yuel Rho),조맹효(Maenghyo Cho) 대한기계학회 2005 대한기계학회 춘추학술대회 Vol.2005 No.11

The linkage framework of surface geometric modeling and analysis based on the NURBS technology is developed in this study. The NURBS surfaces are generated by interpolating given set of data points or by extracting the necessary information to construct the NURBS surface from the IGES file which is generated by the commercial CAD systems in the present study. Some numerical examples that show the tendency of displacement convergence according to the paramterization method of the NURBS surface are given. And quadric shape surfaces which is generated exactly based on NURBS representation is considered. It is the one of the advantages of the NURBS equation to express quadric shape curves or surfaces exactly in the mathematical point of view. A trimmed surfaces which are often encountered during modeling process in the CAD systems are handled briefly in the present study.

쉘 해석과 곡면 모델링의 연동

조맹효,최진복,노희열,Cho, Maeng-Hyo,Choi, Jin-Bok,Roh, Hee-Yuel 한국전산구조공학회 2007 한국전산구조공학회논문집 Vol.20 No.2

본 연구에서는 NURBS곡면식을 바탕으로 하는 곡면 모델링과 쉘 유한요소해석의 효율적인 연동체계를 개발하고자 한다. 기하학적으로 정확한 쉘 유한요소해석에서 정확한 기하량의 계산은 필수적이며, 따라서 곡면을 표현하는 일반적인 방법인 NURBS곡면식으로 부터 필요한 기하량을 직접 계산한다면 보간에 의해 발생할 수 있는 기하학적 오차를 줄임으로써 해의 수렴성을 높일 수 있다. 아울러 기하학적으로 정확한 쉘 유한요소를 일반적인 곡면에 적용하기 힘들었던 한계점을 극복하여 수학적으로 표현 가능한 단순한 곡면들뿐만 아니라, NURB곡면식으로 표현 가능한 일반적인 곡면의 해석이 가능하게 되어 적용범위를 확장할 수 있다. 본 연구에서는 곡면을 생성함에 있어 주어진 데이터 점들을 보간하여 NURBS곡면을 생성하는데, 이러한 데이터들은 일반적으로 곡면의 스캐닝을 통해 얻을 수 있다. 곡면을 보간하여 NURBS곡면을 생성하는 과정에서 사용되는 매개변수 정의방식에 때라 생성된 곡면의 정확성이 차이를 보이므로 곡면의 형상에 따라 적합한 방식을 사용하여 곡면을 보간 할 필요가 있다. 몇 가지 잘 알려진 수치예제를 통하여 개발된 연동체계의 성능과 정확성을 검증하고 그 결과를 비교 분석하였다. The linkage framework of surface geometric modeling based on the NURBS and shell finite element analysis is developed in this study. In the geometrically exact shell finite element analysis, the accuracy of the analysis strongly depends upon the accurate computation of the surface geometric quantities. Therefore if we obtain the necessary geometric quantities from the NVRBS surface equation, it's possible to construct the effective linkage framework of surface modeling in the CAD systems and shell finite element analysis using geometrically exact shell finite element. Besides, the linkage framework can be applied to the analysis of general and complex surfaces as well as simple surfaces. In this study, the shell surfaces are generated by interpolating given set of data points based on the NURBS surfaces. These data points usually can be obtained from surface scanning. But the representations of the generated NURBS surface are not same to one another. The accuracy depends on the chosen parameterization methods used in NURBS. Therefore, it is needed to select the suitable parameterization method according to the geometry of the surfaces. To verify the performance and accuracy of our developed linkage framework, we solve several well-known benchmark problems and assess the performance of the developed method.

표면효과를 고려한 박막구조의 멀티스케일 해석

조맹효,최진복,정광섭,Cho, Maeng-Hyo,Choi, Jin-Bok,Jung, Kwang-Sub 한국전산구조공학회 2007 한국전산구조공학회논문집 Vol.20 No.3

In general, the response of bulk material is independent of its size when it comes to considering classical elasticity theory. Because the surface to bulk ratio of the large solids is very small, the influence of surface can be negligible. But the surface effect plays important role as the surface to bulk ratio becomes larger, that is, the contribution of the surface effect must be considered in nano-size elements such as thin film or beam structure. Molecular dynamics computation has been a conventional way to analyze these ultra-thin structures but this method is limited to simulate on the order of $10^6{\sim}10^9$ atoms for a few nanoseconds, and besides, very time consuming. Analysis of structures in submicro to micro range(thin-film, wire etc.) is difficult with classical molecular dynamics due to the restriction of computing resources and time. Therefore, in this paper, the continuum-based method is considered to simulate the overall physical and mechanical properties of the structures in nano-scale, especially, for the thin-film. 일반적으로 고전적인 탄성이론에서 매크로 스케일의 구조물의 물성은 구조물의 사이즈에 영향을 받지 않는다. 그 이유는 구조물 전체 체적에 대한 표면의 비율이 매우 작기 때문에 표면의 효과를 무시할 수 있기 때문이다. 그러나, 구조물 전체의 부피에 대한 표면의 비율이 커지게 되면 표면의 효과가 매우 중요한 역할을 하게 되며 지배적으로 나타나게 된다. 특히 나노 박막이나 나노 빔 등 나노 스케일의 구조물에서는 표면효과의 영향을 반드시 고려하여야만 한다. 분자 동역학 시뮬레이션은 이러한 나노 스케일의 구조물 역학적 해석을 위해서 그간 사용되어 온 일반적인 방법이었으나, 과도하게 요구되는 계산시간과 전산자원의 한계로 인해 여전히 수 나노 초 동안에 $10^6{\sim}10^9$개의 원자들에 대한 시뮬레이션이 가능한 정도이다. 따라서 실제적으로 MEMS/NEMS 분야에서 사용되는 서브마이크 스케일에서 마이크로 스케일의 구조물의 분자동역학 시뮬레이션을 통한 해석은 가능하나 설계를 목적으로 했을 때는 현실적이지 못하다. 따라서 본 연구에서는 이러한 분자 동역학 시뮬레이션 기법의 단점을 보완하고자 나노 스케일의 매우 작은 구조물에서 지배적으로 나타나는 표면효과를 고려할 수 있는 연속체 기반의 모델을 제시하고자 한다. 특히 본 논문에서는 박막구조물의 해석을 위하여 고전적인 Kirchhoff 평판이론을 바탕으로 표면효과를 고려할 수 있도록 하는 연속체 모델을 제안하고 이를 바탕으로 유한요소해석을 수행하여 그 해석 결과를 분자 동역학 시뮬레이션 결과와 비교하였다.

A Taxonomic Study of Order Arcellinida (Protozoa: Sarcomastigophora: Rhizopoda) from Korea (Ⅱ)

Wan-Ho Chung(鄭玩鎬),Jin-Bok Choi(崔鎭福) 한국동물분류학회 1995 Animal Systematics, Evolution and Diversity Vol.11 No.3

A Taxonomic Study of Orders Arcellinida and Gromiida (Protozoa: Sarcomastigophora: Rhizopoda) from Ch'ŏngju Area, Korea

Chung, Wan-Ho(鄭玩鎬),Choi, Jin-Bok(崔鎭福) 한국동물분류학회 1989 Animal Systematics, Evolution and Diversity Vol.5 No.2

A Taxonomic Study of Order Arcellinida (Protozoa: Sarcomastigophora: Rhizopoda) from Korea

Chung, Wan-Ho(鄭玩鎬),Kang, Sok-Bon(姜錫本),Choi, Jin-Bok(崔鎭福) 한국동물분류학회 1992 Animal Systematics, Evolution and Diversity Vol.8 No.1

축소 시스템과 부구조화 기법에 기초한 대형 구조물 해석 기법 연구

김현기(Hyun-Gi Kim),백승민(Seung-Min Baek),최진복(Jin-Bok Choi),조맹효(Meang-Hyo Cho),김혁(Hyuk Kim),최형길(Hyoung-Gil Choi),최재락(Jae-Rack Choi) 한국자동차공학회 2005 한국자동차공학회 Symposium Vol.- No.-

A number of approximate techniques have been proposed to calculate the eigenvalues in a reduced manner. These schemes approximate the lower eigenvalues that represent the global behavior of the structures. But, the reduction methods are not efficient to be applied to large scale problems. The selection of the primary degrees of freedom might be localized causing the excessive emphasis of the lower mode or lost of the important modes. Moreover, it takes considerable amount of computing time for the construction of the reduced system in large-scale problem. This paper proposes the reduced system combined with the sub-structuring scheme based on the primary degrees of freedom. For the construction of the final reduced system, the system of each domain subdivided into primary, slave and interface degrees of freedom It is remarkably efficient in computing time accurate compared to full-scale system. Numerical examples demonstrate that the proposed method saves computational cost effectively and provides a reduced system which predicts the accurate eigenpairs of global system.