Elastic nonlinear stability analysis of thin rectangular plates through a semi-analytical approach

I. Shufrin, O. Rabinovitch, M. Eisenberger

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

A semi-analytical approach to the elastic nonlinear stability analysis of rectangular plates is developed. Arbitrary boundary conditions and general out-of-plane and in-plane loads are considered. The geometrically nonlinear formulation for the elastic rectangular plate is derived using the thin plate theory with the nonlinear von Kármán strains and the variational multi-term extended Kantorovich method. Emphasis is placed on the effect of destabilizing loads and on the derivation of the solution methodologies required for tracking a highly nonlinear equilibrium path, namely: parameter continuation and arc-length continuation procedures. These procedures, which are commonly used for the solution of discretized structural systems governed by nonlinear algebraic equations, are augmented and generalized for the direct application to the PDE. The boundary value problem that results from the arc-length continuation scheme and consists of coupled differential, integral, and algebraic equations is re-formulated in a form that allows the use of standard numerical BVP solvers. The performance of the continuation procedures and the convergence of the multi-term extended Kantorovich method are examined through the solution of the two-dimensional Bratu-Gelfand benchmark problem. The applicability of the proposed approach to the tracking of the nonlinear equilibrium path in the post-buckling range is demonstrated through numerical examples of rectangular plates with various boundary conditions.

Original languageEnglish
Pages (from-to)2075-2092
Number of pages18
JournalInternational Journal of Solids and Structures
Volume46
Issue number10
DOIs
StatePublished - 15 May 2009
Externally publishedYes

Keywords

  • Arc-length continuation
  • Extended Kantorovich method
  • Geometrically nonlinear stability analysis
  • Parameter continuation
  • Semi-analytical approach

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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