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

In linear isogeometric analysis of beams, the success of selective reduced integration and 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, C0-continuous NURBS selective reduced integration and 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 B¯ formulation offers higher accuracy, and the proper recovery of strain measures and cross-sectional stress resultants.