TY - JOUR

T1 - Non-dimensional analysis of a two-dimensional beam using linear stiffness matrix in absolute nodal coordinate formulation

AU - Kim, Kun Woo

AU - Lee, Jae Wook

AU - Jang, Jin Seok

AU - Oh, Joo Young

AU - Kang, Ji Heon

AU - Kim, Hyung Ryul

AU - Yoo, Wan Suk

N1 - Publisher Copyright:
© 2017 The Korean Society of Mechanical Engineers.

PY - 2017/1

Y1 - 2017/1

N2 - Absolute nodal coordinate formulation was developed in the mid-1990s, and is used in the flexible dynamic analysis. In the process of deriving the equation of motion, if the order of polynomial referring to the displacement field increases, then the degrees of freedom increase, as well as the analysis time increases. Therefore, in this study, the primary objective was to reduce the analysis time by transforming the dimensional equation of motion to a nondimensional equation of motion. After the shape function was rearranged to be non-dimensional and the nodal coordinate was rearranged to be in length dimension, the non-dimensional mass matrix, stiffness matrix, and conservative force was derived from the non-dimensional variables. The verification and efficiency of this nondimensional equation of motion was performed using two examples; cantilever beam which has the exact solution about static deflection and flexible pendulum.

AB - Absolute nodal coordinate formulation was developed in the mid-1990s, and is used in the flexible dynamic analysis. In the process of deriving the equation of motion, if the order of polynomial referring to the displacement field increases, then the degrees of freedom increase, as well as the analysis time increases. Therefore, in this study, the primary objective was to reduce the analysis time by transforming the dimensional equation of motion to a nondimensional equation of motion. After the shape function was rearranged to be non-dimensional and the nodal coordinate was rearranged to be in length dimension, the non-dimensional mass matrix, stiffness matrix, and conservative force was derived from the non-dimensional variables. The verification and efficiency of this nondimensional equation of motion was performed using two examples; cantilever beam which has the exact solution about static deflection and flexible pendulum.

KW - Absolute Nodal Coordinate Formulation

KW - Linear Stiffness Matrix

KW - Non-Dimensional Analysis

KW - Two-Dimensional Beam

UR - http://www.scopus.com/inward/record.url?scp=85018987587&partnerID=8YFLogxK

U2 - 10.3795/KSME-A.2017.41.1.031

DO - 10.3795/KSME-A.2017.41.1.031

M3 - Article

AN - SCOPUS:85018987587

SN - 1226-4873

VL - 41

SP - 31

EP - 40

JO - Transactions of the Korean Society of Mechanical Engineers, A

JF - Transactions of the Korean Society of Mechanical Engineers, A

IS - 1

ER -