Efficiency of non-dimensional analysis for absolute nodal coordinate formulation

Absolute nodal coordinate formulation was developed in the mid-1990s. The adoption of the continuum mechanics concept has allowed large displacements and large deformations to be expressed in flexible body analysis. However, the analysis time increases due to the increased number of degrees of freed...

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Bibliographic Details
Published in:Nonlinear dynamics 2017-01, Vol.87 (2), p.1139-1151
Main Authors: Kim, Kun-Woo, Lee, Jae-Wook, Jang, Jin-Seok, Oh, Joo-Young, Kang, Ji-Heon, Kim, Hyung-Ryul, Yoo, Wan-Suk
Format: Article
Language:English
Subjects:
Automotive Engineering
Cantilever beams
Classical Mechanics
Continuum mechanics
Control
Deflection
Deformation
Dimensional analysis
Dynamical Systems
Engineering
Equations of motion
Exact solutions
Flexible bodies
Mass matrix
Mathematical analysis
Mathematical models
Matrix algebra
Matrix methods
Mechanical Engineering
Nonlinear dynamics
Original Paper
Pendulums
Stiffness matrix
Vibration
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Summary:Absolute nodal coordinate formulation was developed in the mid-1990s. The adoption of the continuum mechanics concept has allowed large displacements and large deformations to be expressed in flexible body analysis. However, the analysis time increases due to the increased number of degrees of freedom at nodal points. Therefore, we aimed to reduce the analysis time by converting a dimensional equation of motion (EOM) to a non-dimensional EOM by using non-dimensional variables of time, length, and force. A non-dimensional mass matrix, a non-dimensional longitudinal stiffness matrix, and a non-dimensional conservative force vector are derived and applied to the non-dimensional EOM. To verify the non-dimensional EOM, a cantilever beam with static deflection, for which an exact solution exists, is considered. As the number of elements is increased, the mean value by the non-dimensional EOM converges to the static deflection. Revolute and spherical joints are used to propose two- and three-dimensional numerical solutions based on the non-dimensional EOM of a free-falling pendulum. These solutions are compared with the numerical solutions from using a dimensional EOM in order to verify the non-dimensional EOM. The analysis results for simple pendulum motion using dimensional and non-dimensional EOMs are in good agreement.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-016-3104-7