An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors

Myung-Jin Choi; Roger Sauer; Sven Klinkel

doi:10.1016/j.cma.2021.113993

An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors

Abstract

An isogeometric finite element formulation for geometrically and materially nonlinear Timoshenko beams is presented, which incorporates in-plane deformation of the cross-section described by two extensible director vectors. Since those directors belong to the space R3, a configuration can be additively updated. The developed formulation allows direct application of nonlinear three-dimensional constitutive equations without zero stress conditions. Especially, the significance of considering correct surface loads rather than applying an equivalent load directly on the central axis is investigated. Incompatible linear in-plane strain components for the cross-section have been added to alleviate Poisson locking by using an enhanced assumed strain (EAS) method. In various numerical examples exhibiting large deformations, the accuracy and efficiency of the presented beam formulation is assessed in comparison to brick elements. We particularly use hyperelastic materials of the St.Venant-Kirchhoff and compressible Neo- Hookean types.

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DOI:: Digital Object Identifier (open in new tab) 10.1016/j.cma.2021.113993
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Keywords

TIMOSHENKO BEAM, GEOMETRIC AND MATERIAL NONLINEARITY, EXTENSIBLE DIRECTORS, SURFACE LOADS, EAS METHOD, ISOGEOMETRIC ANALYSIS

Details

Category:: Articles
Type:: artykuły w czasopismach
Published in:: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING no. 385,
ISSN: 0045-7825
Language:: English
Publication year:: 2021
Bibliographic description:: Choi M., Sauer R., Klinkel S.: An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors// COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING -Vol. 385, (2021), s.113993-
DOI:: Digital Object Identifier (open in new tab) 10.1016/j.cma.2021.113993
Verified by:: Gdańsk University of Technology