Efficiency of non-dimensional analysis for absolute nodal coordinate formulation

• Published in: Nonlinear dynamics Vol. 87; no. 2; pp. 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: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.01.2017; Springer Nature B.V
• 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; Verification of non-dimensional EOM; Continuum mechanics; Absolute nodal coordinate formulation; Analysis efficiency; Non-dimensional analysis
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-016-3104-7

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.