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Application of continuation methods to uniaxially loaded postbuckled plates

Publication ,  Journal Article
Lyman, TC; Virgin, LN; Davis, RB
Published in: Journal of Applied Mechanics, Transactions ASME
January 1, 2014

Continuation methods are used to examine the static and dynamic postbuckled behavior of a uniaxially loaded, simply supported plate. Continuation methods have been extensively used to study problems in mathematics and physics; however, they have not been as widely applied to problems in engineering. When paired with a Galerkin approximation, continuation methods are shown to be well suited to solving nonlinear buckling problems. In addition to providing a robust solution method for nonlinear equations, the linearized Jacobians from the continuation steps will contain natural frequency and mode shape information for mechanical systems (provided inertia terms are included). Results for the primary buckling branch are compared to previously published results. Using the open-source continuation package Auto, stable, remote secondary buckling branches were discovered. These secondary stable equilibrium persist even in the presence of geometric imperfections and their existence is confirmed by experiment. Copyright © 2014 by ASME.

Duke Scholars

Published In

Journal of Applied Mechanics, Transactions ASME

DOI

EISSN

1528-9036

ISSN

0021-8936

Publication Date

January 1, 2014

Volume

81

Issue

3

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 4001 Aerospace engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
  • 0901 Aerospace Engineering
 

Citation

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Lyman, T. C., Virgin, L. N., & Davis, R. B. (2014). Application of continuation methods to uniaxially loaded postbuckled plates. Journal of Applied Mechanics, Transactions ASME, 81(3). https://doi.org/10.1115/1.4024672
Lyman, T. C., L. N. Virgin, and R. B. Davis. “Application of continuation methods to uniaxially loaded postbuckled plates.” Journal of Applied Mechanics, Transactions ASME 81, no. 3 (January 1, 2014). https://doi.org/10.1115/1.4024672.
Lyman TC, Virgin LN, Davis RB. Application of continuation methods to uniaxially loaded postbuckled plates. Journal of Applied Mechanics, Transactions ASME. 2014 Jan 1;81(3).
Lyman, T. C., et al. “Application of continuation methods to uniaxially loaded postbuckled plates.” Journal of Applied Mechanics, Transactions ASME, vol. 81, no. 3, Jan. 2014. Scopus, doi:10.1115/1.4024672.
Lyman TC, Virgin LN, Davis RB. Application of continuation methods to uniaxially loaded postbuckled plates. Journal of Applied Mechanics, Transactions ASME. 2014 Jan 1;81(3).

Published In

Journal of Applied Mechanics, Transactions ASME

DOI

EISSN

1528-9036

ISSN

0021-8936

Publication Date

January 1, 2014

Volume

81

Issue

3

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 4001 Aerospace engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
  • 0901 Aerospace Engineering