절대절점좌표계에서 박판에 대한 무차원 변형에너지 정의

국문 초록 (Abstract)

절대절점좌표계는 1990년대 중반 탄성 다물체 동역학 해석을 위해 개발된 기법으로 대변위, 대회전 그리고 대변형의 표현이 가능하다. 이러한 장점에도 불구하고 자유도의 증가로 인한 해석시간의 증가라는 단점이 존재한다. 해석시간을 줄이는 방안들 중 하나로 무차원 운동방정식이 적용되어 왔다. 본 연구에서는 절대절점좌표계에서 박판에 대한 무차원 운동방정식을 활용하여 그 효율성을 확인하였다. 무차원 질량행렬과 힘벡터를 유도하는 과정은 생략하였으며, 무차원 강성행렬을 유도하는 과정에 대해 설명하였다. 중력장에서 구 조인트로 체결된 박판의 거동을 확인하였으며, 요소수가 증가할수록 차원 운동방정식 대비 무차원 운동방정식의 해석시간이 단축되는 것을 확인하였다.

다국어 초록 (Multilingual Abstract)

The absolute nodal coordinate formulation is a technique developed for the analysis of flexible multibody dynamics in the mid-1990s, and it is possible to express large displacement, rotation and deformation. Despite these advantages, there is a disadvantage of an increase in analysis time due to an increase in degrees of freedom. A nondimensional equation of motion has been applied as one of the methods to reduce the analysis time. In this study, the efficiency was confirmed by using the non-dimensional equation of motion for the thin plate in the absolute nodal coordinate system. The process of deriving the non-dimensional mass matrix and force vector was omitted, and the process of deriving the non-dimensional stiffness matrix was explained. The behavior of thin plate fastened with spherical joints in the gravitational field was confirmed, and it was confirmed that as the number of elements increased, the analysis time of the non-dimensional equations of motion was shortened compared to the dimensional equations of motion.

목차 (Table of Contents)

• 초록
• Abstract
• 1. 서론
• 2. 무차원 변형에너지 정의
• 3. 무차원 변형에너지의 검증과 효율성
• 4. 결론
• 참고문헌(References)

참고문헌 (Reference)

1 강지헌, "절대절점좌표계에서 대변형 탄성 보의 무차원 변형에너지 정의" 대한기계학회 42 (42): 643-648, 2018

2 Reddy, J. N., "Theory and Analysis of Elastic Plates and Shells" CRC Press 2007

3 Kun-Woo Kim, "The motion and deformation rate of a flexible hose connected to a mother ship" 대한기계학회 26 (26): 703-710, 2012

4 Kawaguti, K., "The Study of the Tether Motion with Time-Varying Length Using the Absolute Nodal Coordinate Formulation with Multiple Nonlinear Time Scales" 1 (1): 491-500, 2007

5 Sugiyama, H., "Nonlinear Elastic Ring Tire Model Using the Absolute Nodal Coordinate Formulation" 223 (223): 211-219, 2009

6 Lacarbonara, W, "Nonlinear Dynamics of Structures" Springer 1 : 2019

7 Omar, M. A., "Multibody System Modeling of Leaf Springs" 10 (10): 1601-1638, 2004

8 Dmitrochenko, O., "Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation" 10 (10): 17-43, 2003

9 Kim, K. W., "Efficiency of Non-Dimensional Analysis for Absolute Nodal Coordinate Formulation" 87 : 1139-1151, 2017

10 Shabana, A. A., "Dynamics of Multibody Systems" Cambridge University Press 2005

11 Shabana, A. A., "Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation" 1 : 339-348, 1997

12 Dufva, K., "Analysis of Thin Plate Structures Using the Absolute Nodal Coordinates Formulation" 219 (219): 345-355, 2005

13 Shabana, A. A., "An Absolute Nodal Coordination for the Large Rotation and Large Deformation Analysis of Flexible Bodies" University of Illinois at Chicago 1996

14 Matikainen, M. K., "A Study of Moderately Thick Quadrilateral Plate Elements based on the Absolute Nodal Coordinate Formulation" 31 (31): 309-338, 2013

15 Yoo, W. S., "A New Thin Spatial Beam Element Using the Absolute Nodal Coordinates : Application to Rotating Strip" 33 (33): 399-422, 2005

16 Newmark, N. M., "A Method of Computation for Structural Dynamics" 85 (85): 67-94, 1959