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Finite element analysis of post-buckling dynamics in plates-Part I: An asymptotic approach

Publication ,  Journal Article
Chen, H; Virgin, LN
Published in: International Journal of Solids and Structures
June 1, 2006

Various static and dynamic aspects of post-buckled thin plates, including the transition of buckled patterns, post-buckling dynamics, secondary bifurcation, and dynamic snapping (mode jumping phenomenon), are investigated systematically using asymptotical and non-stationary finite element methods. In part I, the secondary dynamic instability and the local post-secondary buckling behavior of thin rectangular plates under generalized (mechanical and thermal) loading is investigated using an asymptotic numerical method which combines Koiter's nonlinear instability theory with the finite element technique. A dynamic multi-mode reduction method-similar to its static single-mode counterpart: Liapunov-Schmidt reduction-is developed in this perturbation approach. Post-secondary buckling equilibrium branches are obtained by solving the reduced low-dimensional parametric equations and their stability properties are determined directly by checking the eigenvalues of the resulting Jacobian matrix. Typical post-secondary buckling forms-transcritical, supercritical and subcritical bifurcations are observed according to different combinations of boundary conditions and load types. Geometric imperfection analysis shows that not only the secondary bifurcation load but also changes in the fundamental post-secondary buckling behavior are affected. The post-buckling dynamics and the global analysis of mode jumping of the plates are addressed in part II. © 2005 Elsevier Ltd. All rights reserved.

Duke Scholars

Published In

International Journal of Solids and Structures

DOI

ISSN

0020-7683

Publication Date

June 1, 2006

Volume

43

Issue

13

Start / End Page

3983 / 4007

Related Subject Headings

  • Mechanical Engineering & Transports
  • 40 Engineering
  • 09 Engineering
 

Citation

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Chen, H., & Virgin, L. N. (2006). Finite element analysis of post-buckling dynamics in plates-Part I: An asymptotic approach. International Journal of Solids and Structures, 43(13), 3983–4007. https://doi.org/10.1016/j.ijsolstr.2005.04.036
Chen, H., and L. N. Virgin. “Finite element analysis of post-buckling dynamics in plates-Part I: An asymptotic approach.” International Journal of Solids and Structures 43, no. 13 (June 1, 2006): 3983–4007. https://doi.org/10.1016/j.ijsolstr.2005.04.036.
Chen H, Virgin LN. Finite element analysis of post-buckling dynamics in plates-Part I: An asymptotic approach. International Journal of Solids and Structures. 2006 Jun 1;43(13):3983–4007.
Chen, H., and L. N. Virgin. “Finite element analysis of post-buckling dynamics in plates-Part I: An asymptotic approach.” International Journal of Solids and Structures, vol. 43, no. 13, June 2006, pp. 3983–4007. Scopus, doi:10.1016/j.ijsolstr.2005.04.036.
Chen H, Virgin LN. Finite element analysis of post-buckling dynamics in plates-Part I: An asymptotic approach. International Journal of Solids and Structures. 2006 Jun 1;43(13):3983–4007.
Journal cover image

Published In

International Journal of Solids and Structures

DOI

ISSN

0020-7683

Publication Date

June 1, 2006

Volume

43

Issue

13

Start / End Page

3983 / 4007

Related Subject Headings

  • Mechanical Engineering & Transports
  • 40 Engineering
  • 09 Engineering