Derivation of Non-dimensional Equation of Motion for Thin Plate in Absolute Nodal Coordinate Formulation

Kun Woo Kim; Jae Wook Lee; Jin Seok Jang; Ji Heon Kang; Wan Suk Yoo

doi:10.1007/978-3-030-34713-0_45

Derivation of Non-dimensional Equation of Motion for Thin Plate in Absolute Nodal Coordinate Formulation

Kun Woo Kim
, Jae Wook Lee
, Jin Seok Jang
, Ji Heon Kang
, Wan Suk Yoo

Department of Smart Mobility Engineering

Korea Institute of Industrial Technology
Pusan National University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

The absolute nodal coordinate formulation was developed in the mid- 1990s to express large deformations and large rotations in flexible multi-body dynamics. It is a non-incremental finite-element procedure wherein the mass matrix is expressed as a constant while the stiffnessmatrix carries highly nonlinear features. The formulation for a thin plate can be developed on the basis of continuum or structural mechanics similar to that for a beam. Absolute nodal coordinate formulation necessarily uses the global slope vector, and this results in an increase in the degree of freedom. In this study, to reduce analysis time, the non-dimensional equation of motion of a thin plate is derived from the dimensional equation of motion using non-dimensional variables. An example of a thin cantilever plate is used to present the improved efficiency of analysis due to the non-dimensional equation of motion, and the simulations are shown with various numbers of elements. The non-dimensional equation of motion is thus verified by demonstrating the similarities of the solutions for both the dimensional and non-dimensional equations of motion.

Original language	English
Title of host publication	Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019
Editors	Walter Lacarbonara, Balakumar Balachandran, Jun Ma, J.A. Tenreiro Machado, Gabor Stepan
Publisher	Springer Nature
Pages	449-459
Number of pages	11
ISBN (Electronic)	9783030347123
DOIs	https://doi.org/10.1007/978-3-030-34713-0_45
State	Published - 2020
Event	1st International Nonlinear Dynamics Conference, NODYCON 2019 - Rome, Italy Duration: 17 Feb 2019 → 20 Feb 2019

Publication series

Name	Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019

Conference

Conference	1st International Nonlinear Dynamics Conference, NODYCON 2019
Country/Territory	Italy
City	Rome
Period	17/02/19 → 20/02/19

Keywords

Absolute nodal coordinate formulation
Non-dimensional equation of motion
Thin plate

Access to Document

10.1007/978-3-030-34713-0_45

Cite this

Kim, K. W., Lee, J. W., Jang, J. S., Kang, J. H., & Yoo, W. S. (2020). Derivation of Non-dimensional Equation of Motion for Thin Plate in Absolute Nodal Coordinate Formulation. In W. Lacarbonara, B. Balachandran, J. Ma, J. A. Tenreiro Machado, & G. Stepan (Eds.), Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019 (pp. 449-459). (Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019). Springer Nature. https://doi.org/10.1007/978-3-030-34713-0_45

Kim, Kun Woo ; Lee, Jae Wook ; Jang, Jin Seok et al. / Derivation of Non-dimensional Equation of Motion for Thin Plate in Absolute Nodal Coordinate Formulation. Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019. editor / Walter Lacarbonara ; Balakumar Balachandran ; Jun Ma ; J.A. Tenreiro Machado ; Gabor Stepan. Springer Nature, 2020. pp. 449-459 (Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019).

@inproceedings{971e526123304d42a94bbefcda83b219,

title = "Derivation of Non-dimensional Equation of Motion for Thin Plate in Absolute Nodal Coordinate Formulation",

abstract = "The absolute nodal coordinate formulation was developed in the mid- 1990s to express large deformations and large rotations in flexible multi-body dynamics. It is a non-incremental finite-element procedure wherein the mass matrix is expressed as a constant while the stiffnessmatrix carries highly nonlinear features. The formulation for a thin plate can be developed on the basis of continuum or structural mechanics similar to that for a beam. Absolute nodal coordinate formulation necessarily uses the global slope vector, and this results in an increase in the degree of freedom. In this study, to reduce analysis time, the non-dimensional equation of motion of a thin plate is derived from the dimensional equation of motion using non-dimensional variables. An example of a thin cantilever plate is used to present the improved efficiency of analysis due to the non-dimensional equation of motion, and the simulations are shown with various numbers of elements. The non-dimensional equation of motion is thus verified by demonstrating the similarities of the solutions for both the dimensional and non-dimensional equations of motion.",

keywords = "Absolute nodal coordinate formulation, Non-dimensional equation of motion, Thin plate",

author = "Kim, \{Kun Woo\} and Lee, \{Jae Wook\} and Jang, \{Jin Seok\} and Kang, \{Ji Heon\} and Yoo, \{Wan Suk\}",

note = "Publisher Copyright: {\textcopyright} 2020 Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019. All rights reserved.; 1st International Nonlinear Dynamics Conference, NODYCON 2019 ; Conference date: 17-02-2019 Through 20-02-2019",

year = "2020",

doi = "10.1007/978-3-030-34713-0\_45",

language = "English",

series = "Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019",

publisher = "Springer Nature",

pages = "449--459",

editor = "Walter Lacarbonara and Balakumar Balachandran and Jun Ma and \{Tenreiro Machado\}, J.A. and Gabor Stepan",

booktitle = "Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019",

address = "Switzerland",

}

Kim, KW, Lee, JW, Jang, JS, Kang, JH & Yoo, WS 2020, Derivation of Non-dimensional Equation of Motion for Thin Plate in Absolute Nodal Coordinate Formulation. in W Lacarbonara, B Balachandran, J Ma, JA Tenreiro Machado & G Stepan (eds), Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019. Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019, Springer Nature, pp. 449-459, 1st International Nonlinear Dynamics Conference, NODYCON 2019, Rome, Italy, 17/02/19. https://doi.org/10.1007/978-3-030-34713-0_45

Derivation of Non-dimensional Equation of Motion for Thin Plate in Absolute Nodal Coordinate Formulation. / Kim, Kun Woo; Lee, Jae Wook; Jang, Jin Seok et al.
Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019. ed. / Walter Lacarbonara; Balakumar Balachandran; Jun Ma; J.A. Tenreiro Machado; Gabor Stepan. Springer Nature, 2020. p. 449-459 (Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Derivation of Non-dimensional Equation of Motion for Thin Plate in Absolute Nodal Coordinate Formulation

AU - Kim, Kun Woo

AU - Lee, Jae Wook

AU - Jang, Jin Seok

AU - Kang, Ji Heon

AU - Yoo, Wan Suk

PY - 2020

Y1 - 2020

N2 - The absolute nodal coordinate formulation was developed in the mid- 1990s to express large deformations and large rotations in flexible multi-body dynamics. It is a non-incremental finite-element procedure wherein the mass matrix is expressed as a constant while the stiffnessmatrix carries highly nonlinear features. The formulation for a thin plate can be developed on the basis of continuum or structural mechanics similar to that for a beam. Absolute nodal coordinate formulation necessarily uses the global slope vector, and this results in an increase in the degree of freedom. In this study, to reduce analysis time, the non-dimensional equation of motion of a thin plate is derived from the dimensional equation of motion using non-dimensional variables. An example of a thin cantilever plate is used to present the improved efficiency of analysis due to the non-dimensional equation of motion, and the simulations are shown with various numbers of elements. The non-dimensional equation of motion is thus verified by demonstrating the similarities of the solutions for both the dimensional and non-dimensional equations of motion.

AB - The absolute nodal coordinate formulation was developed in the mid- 1990s to express large deformations and large rotations in flexible multi-body dynamics. It is a non-incremental finite-element procedure wherein the mass matrix is expressed as a constant while the stiffnessmatrix carries highly nonlinear features. The formulation for a thin plate can be developed on the basis of continuum or structural mechanics similar to that for a beam. Absolute nodal coordinate formulation necessarily uses the global slope vector, and this results in an increase in the degree of freedom. In this study, to reduce analysis time, the non-dimensional equation of motion of a thin plate is derived from the dimensional equation of motion using non-dimensional variables. An example of a thin cantilever plate is used to present the improved efficiency of analysis due to the non-dimensional equation of motion, and the simulations are shown with various numbers of elements. The non-dimensional equation of motion is thus verified by demonstrating the similarities of the solutions for both the dimensional and non-dimensional equations of motion.

KW - Absolute nodal coordinate formulation

KW - Non-dimensional equation of motion

KW - Thin plate

UR - https://www.scopus.com/pages/publications/85125620828

U2 - 10.1007/978-3-030-34713-0_45

DO - 10.1007/978-3-030-34713-0_45

M3 - Conference contribution

AN - SCOPUS:85125620828

T3 - Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019

SP - 449

EP - 459

BT - Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019

A2 - Lacarbonara, Walter

A2 - Balachandran, Balakumar

A2 - Ma, Jun

A2 - Tenreiro Machado, J.A.

A2 - Stepan, Gabor

PB - Springer Nature

T2 - 1st International Nonlinear Dynamics Conference, NODYCON 2019

Y2 - 17 February 2019 through 20 February 2019

ER -

Kim KW, Lee JW, Jang JS, Kang JH, Yoo WS. Derivation of Non-dimensional Equation of Motion for Thin Plate in Absolute Nodal Coordinate Formulation. In Lacarbonara W, Balachandran B, Ma J, Tenreiro Machado JA, Stepan G, editors, Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019. Springer Nature. 2020. p. 449-459. (Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019). doi: 10.1007/978-3-030-34713-0_45

Derivation of Non-dimensional Equation of Motion for Thin Plate in Absolute Nodal Coordinate Formulation

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this