Nondimensional modelling of 2D beam for slope discontinuity problem in ANCF
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DOI 10.1007/s12206-020-0806-z
Journal of Mechanical Science and Technology 34 (9) 2020 Original Article DOI 10.1007/s12206-020-0806-z Keywords: · Nondimensional modelling · Slope discontinuity · Absolute nodal coordinate formulation · 2D beam · Verification and efficiency
Correspondence to: Kunwoo Kim [email protected]
Citation: Kang, J., Lee, J., Jang, J., Choi, C., Kim, K. (2020). Nondimensional modelling of 2D beam for slope discontinuity problem in ANCF. Journal of Mechanical Science and Technology 34 (9) (2020) 3545~3552. http://doi.org/10.1007/s12206-020-0806-z
Received February 19th, 2020 Revised
Nondimensional modelling of 2D beam for slope discontinuity problem in ANCF Jiheon Kang1, Jaewook Lee2, Jinseok Jang2, Changyoung Choi2 and Kunwoo Kim2 1
2
Department of Mechanical Engineering, Pusan National University, Busan 46241, Korea, Daegyeong Division, Korea Institute of Industrial Technology, Daegu 42994, Korea
Abstract
Various mechanical and structural systems possess slope discontinuity. Some bodies with slope discontinuity can be modeled using absolute nodal coordinate formulation, which can accurately express the rigid body mode when using the element and global shape functions. However, at the intersection of slope discontinuities, it is not easy to construct the equation of motion because the orientation changes. The problem of modeling at the intersection can be solved by defining the global slope vector in the body coordinate system instead of the element coordinate system. The analysis time in absolute nodal coordinate formulation is mostly greater than that in floating frame of reference formulation owing to the highly non-linear stiffness matrix. In this study, based on the work of Shabana and Mikkola, the analysis efficiency was demonstrated using the nondimensional model for the slope discontinuity problem in the absolute node coordinate system.
June 19th, 2020
Accepted June 24th, 2020 † Recommended by Editor No-cheol Park
© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2020
1. Introduction In the finite element community, the existing incremental approach using infinitesimal and finite rotations was introduced into multibody problems [1]. When using the element shape function, rigid body translation can be represented accurately, but not rigid body rotation. This has also been observed in the linearization of nodal coordinates such that the strain and elastic forces are not zero in the rigid body mode [2]. To solve this problem, the multibody community introduced an intermediate coordinate system to accurately represent the large rotations in rigid bodies [3]. As shown in Fig. 1, the global coordinate system refers to coordinates with fixed or constant translational speeds used to define joints in terms of multibody dynamics. The global coordinate system is also called the Newtonian or inertial reference frame. The body coordinate system may or may not be attached to the body and is used to determine the connectivity conditio
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