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PROCEEDINGS OF THE FOURTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
A General Model for the Analysis of Beams Including Warping Effects
A. Genoese, A. Genoese, A. Bilotta and G. Garcea
DIMES, University of Calabria, Rende (CS), Italy
A. Genoese, A. Genoese, A. Bilotta, G. Garcea, "A General Model for the Analysis of Beams Including Warping Effects", in , (Editors), "Proceedings of the Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 98, 2013. doi:10.4203/ccp.102.98
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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