Enhanced geometrically nonlinear generalized beam theory formulation: derivation, numerical implementation, and illustration

André Dias Martins, Dinar Camotim, Rodrigo Gonçalves, Pedro Borges Dinis

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

This paper enhances the available generalized beam theory (GBT) geometrically nonlinear (elastic) formulations by including (1) the whole set of nonlinear membrane strain terms, and (2) the nonlinear bending strain terms. Initially, the main steps involved in the derivation, development, and numerical implementation of the novel/enhanced GBT geometrically nonlinear formulation are presented in detail. Then, after comparing the proposed and available GBT nonlinear formulations, numerical results concerning two illustrative examples are presented and discussed. They make it possible (1) to better understand the concepts and procedures involved, and (2) to assess the relevance of the added nonlinear membrane and bending strain terms. Such results (1) concern a Z-column and a lipped channel beam under uniform stress resultant diagrams and buckling in distortional and local modes, respectively, and (2) comprise several equilibrium paths obtained from approximate or rigorous analyses, relevant displacement profiles, modal participation diagrams, and deformed configurations. For validation, the GBT-based results are compared with values yielded by shell finite-element analyses.

Original languageEnglish
Article number04018036
JournalJournal of Engineering Mechanics
Volume144
Issue number6
DOIs
Publication statusPublished - 1 Jun 2018

Keywords

  • Beam finite elements
  • Generalized beam theory (GBT)
  • Geometrically nonlinear formulation
  • Thin-walled member behavior

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