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

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 space ${\Bbb R}^3$, a configuration can be additively updated. The developed allows direct application three-dimensional constitutive equations without zero stress conditions. Especially, significance considering correct surface loads rather than applying an equivalent load directly on central axis investigated. Incompatible linear strain components have been added alleviate Poisson locking using enhanced assumed (EAS) method. In various numerical examples exhibiting large deformations, accuracy efficiency presented beam assessed in comparison brick elements. We particularly use hyperelastic materials St. Venant-Kirchhoff compressible Neo-Hookean types.