Locking-free isogeometric Timoshenko–Ehrenfest beam formulations for geometrically nonlinear analysis of planar beam structures

Abstract

In linear isogeometric analysis of beams, the success of selective reduced integration and $\overline{B}$ projection methods in mitigating the locking phenomenon has been proved. This study further extends these methods to the geometrically nonlinear analysis with two isogeometric Timoshenko–Ehrenfest beam formulations, that is, $C^0$-continuous NURBS selective reduced integration and $\overline{B}$ formulations. Three numerical examples are presented examining overall structural responses, strain energy, recovery of cross-sectional stress resultants, and convergence properties. Although the two proposed formulations exhibit the locking-free behavior for highly flexible beam structures, the $\overline{B}$ formulation offers higher accuracy, and the proper recovery of strain measures and cross-sectional stress resultants.

Keywords:

• Isogeometric analysis
• membrane and shear locking effect
• geometrically nonlinear analysis
• planar curved beams
• ${\mathit{C}}^0$-continuous NURBS selective reduced integration
• $\overline{\mathit{B}}$ projection

Acknowledgment

The first author acknowledges the Postdoctoral Fellowship awarded by the Second Century Fund (C2F) from Chulalongkorn University, Thailand.

Additional information

Funding

The first author acknowledges the Postdoctoral Fellowship awarded by the Second Century Fund (C2F) from Chulalongkorn University, Thailand.