Nondimensional analysis of a two-dimensional shear deformable beam in absolute nodal coordinate formulation. (April 2018)

• Record Type: Journal Article
• Authors: Kim, Kun-Woo; Lee, Jae-Wook; Jang, Jin-Seok; Oh, Joo-Young; Kang, Ji-Heon; Kim, Hyung-Ryul; Yoo, Wan-Suk
• Is Part Of: Proceedings of the Institution of Mechanical Engineers. Volume 232:Number 7(2018)
• Page Start: 1236
• Page End: 1246
• Publication Date: 2018-04
• Subjects: Absolute nodal coordinate formulation -- two-dimensional shear deformable beam -- nondimensional analysis -- analysis efficiency -- verification of nondimensional equation of motion; Mechanical engineering -- Periodicals; 621.05
• DOI: 10.1177/0954406217705407
• Languages: English
• ISSNs: 0954-4062

Abstract

Absolute nodal-coordinate formulation is a technique that was developed in 1996 for expressing the large rotation and deformation of a flexible body. It utilizes global slopes without a finite rotation in order to define nodal coordinates. The method has a shortcoming in that the central processing unit time increases because of increases in the degrees of freedom. In particular, when considering the deformation of a cross section, the shortcoming due to the increase in the degrees of freedom becomes clear. Therefore, in the present research, the dimensional equation of motion concerning a two-dimensional shear deformable beam, developed by Omar and Shabana, is converted into a nondimensional equation of motion in order to reduce the central processing unit time. By utilizing an example of a cantilever beam, wherein an exact solution for the static deflection exists, the nondimensional equation of motion was verified. Moreover, by using an example of a free-falling flexible pendulum, the efficiency of the nondimensional equation of motion gained by increasing the number of elements was compared with that of the dimensional equation of motion.