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


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Chen, H; Virgin, LN

Published Date

  • June 1, 2006

Published In

Volume / Issue

  • 43 / 13

Start / End Page

  • 3983 - 4007

International Standard Serial Number (ISSN)

  • 0020-7683

Digital Object Identifier (DOI)

  • 10.1016/j.ijsolstr.2005.04.036

Citation Source

  • Scopus