Keywords: nonuniform warping, Saint-Venant stress field, mixed formulation, corotational strategy, Koiter asymptotic approach.

A geometrically nonlinear model for isotropic and homogeneous beams including the non-uniform out of plane warping deformation of the cross-section due to torsion and shear is derived using the implicit corotational method (ICM). The basic idea of ICM is the application of the corotational method, initially proposed for a whole finite element, at level of the continuum geometrical description. This enable the definition of a general tool to obtain objective models for structural finite elements.

The generalized variational principle of Hellinger-Reissner, requiring a separate description of the stress and displacement fields, is exploited. For each section, a corotational frame is introduced where statics and kinematics are derived from a 3D linear elastic formulation. The latter exactly reproduces the Saint-Venant solution while variable warping effects are added in a simplified but accurate way, making the model suitable for the analysis of beams with either thin-walled or compact crosssections.

A mixed finite element is implemented and used inside a Koiter-like analysis algorithm which is highly sensitive to the geometrical coherence of the formulation. The numerical simulations performed demonstrate the accuracy and effectiveness of the proposed nonlinear beam model.

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