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RESEARCH PAPERS

# Verification of Absolute Nodal Coordinate Formulation in Flexible Multibody Dynamics via Physical Experiments of Large Deformation Problems

[+] Author and Article Information
Wan-Suk Yoo

National Research Laboratory of CAE, Department of Mechanical Engineering,  Pusan National University, 30 San, Jangjeon-dong, Geumjeong-gu, Busan, 609-735, Koreawsyoo@pusan.ac.kr

Su-Jin Park

National Research Laboratory of CAE, Department of Mechanical Engineering,  Pusan National University, 30 San, Jangjeon-dong, Geumjeong-gu, Busan, 609-735, Koreapsjjjk@pusan.ac.kr

Oleg N. Dmitrochenko

Universal Mechanism Laboratory, Department of Applied Mechanics,  Bryansk State Technical University, Bulvar 50-letiya Oktyabrya, 7, Bryansk, 241035, Russiadmitroleg@rambler.ru

Dmitry Yu. Pogorelov

Universal Mechanism Laboratory, Department of Applied Mechanics,  Bryansk State Technical University, Bulvar 50-letiya Oktyabrya, 7, Bryansk, 241035, Russiapogorelov@tu-bryansk.ru

Gradient $φ$ of a scalar function $f(e)$ w.r.t. vector $e$ of its arguments is denoted by $φ=∂f∕∂e$ and considered as a column but not a row vector to avoid multiple transpose signs. Gradient $Φ$ of vector $φ$ is a Jacobian matrix and denoted by $Φ=∂φ∕∂eT=∂f∕∂e∂eT$. The transpose sign here emphasizes that the elements of the second vector are placed in rows.

Such representation is allowable in the case of a thin beam when the moment of inertia of the cross section is small.

J. Comput. Nonlinear Dynam 1(1), 81-93 (May 21, 2005) (13 pages) doi:10.1115/1.2008998 History: Revised May 21, 2005

## Abstract

A review of the current state of the absolute nodal coordinate formulation (ANCF) is proposed for large-displacement and large-deformation problems in flexible multibody dynamics. The review covers most of the known implementations of different kinds of finite elements including thin and thick planar and spatial beams and plates, their geometrical description inherited from FEM, and formulations of the most important elements of equations of motion. Much attention is also paid to simulation examples that show reasonableness and accuracy of the formulations applied to real physical problems and that are compared with experiments having significant geometrical nonlinearity. Current and further development directions of the ANCF are also briefly outlined.

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## Figures

Figure 2

Large-displacement ANCF beam finite element: (a) nodal vectors and (b) co-rotational frame

Figure 3

Dynamical test simulations of two-dimensional beams with large displacements: (a) free falling beam-shaped pendulum (13,16) and (b) flexible ellipsograph with a rigid pendulum (16-17)

Figure 4

Two-dimensional and three-dimensional thick beam elements: (a) two-dimensional element by Omar and Shabana (21) and (b) three-dimensional element by Shabana and Yakoub (23)

Figure 5

Hermitian thin plate elements: (a) standard 16-d.o.f. element and (b) new ANCF 48-d.o.f. element

Figure 6

Experiment and simulation: a plate with a weight

Figure 7

Heavy membrane suspended on three corners: 12, 22, 32, 42, 62 and 82 elements

Figure 1

Two-dimensional beam finite element: (a) standard and (b) parameterized

Figure 15

Experimental and simulated frames of the rotating strip steady motion: (a) intermediate position, (b) experiment, and (c) simulation

Figure 8

Experiment and simulation video frames with a 0.4×0.2m plate with a 0.26kg weight

Figure 9

Free-falling plate-shaped pendulum (from (18))

Figure 10

Deformed state of a triangle plate element and its nodal vectors

Figure 11

Simulation of Dali’s soft clocks by triangles

Figure 12

New finite element of a thin spatial beam

Figure 13

Possible configurations of helicoseir when α=45

Figure 14

The 3rd form of the helicoseir (α=40.8): (a) two-dimensional simulation in ANCF and (b) experimental frames

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