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.
|Journal||Journal of Engineering Mechanics|
|Publication status||Published - 1 Jun 2018|
- Beam finite elements
- Generalized beam theory (GBT)
- Geometrically nonlinear formulation
- Thin-walled member behavior