A corotational based geometrically nonlinear Generalized Beam Theory: buckling FE analysis

A geometrically nonlinear Generalized Beam Theory is formulated and the results in the framework of buckling analyses are discussed. The geometrically nonlinear model is recovered reusing the model available in the linear context. This generalization to the nonlinear context is obtained exploiting the corotational based method called Implicit Corotational Method, starting from a mixed energy description of the continuum in terms of nonlinear Biot stress/strain tensors and using convenient assumptions for the linear stress/strain tensors. Once obtained, the nonlinear model has been implemented using a flexibility based finite element. The results of buckling analyses for different and complex beam cross-section geometries, emphasizing distortional and local buckling behaviors, are presented and comparisons with finite element shell models made.