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Orientador(es)
Resumo(s)
A robust and efficient mixed finite element formulation, applicable to both shear-rigid (Kirchhoff-type) and shear-flexible (Reissner-type) beam theories, is proposed for the geometrically exact planar analysis of beams and frames. The formulation is derived from a Hellinger-Reissner-type variational principle, in which the spatial components of the internal forces, bending moment, and cross-sectional rotation are adopted as primary unknowns. Equilibrium of the spatial internal forces is satisfied in strong form at the member level, while the assumed bending moment field is C0 -continuous and satisfies equilibrium boundary conditions. The formulation is intrinsically free from shear- and membrane-locking phenomena, admits explicit closed-form expressions for both the residual vector and the consistent symmetric tangent matrix, and yields a highly sparse and banded global system with a reduced number of unknowns compared with conventional displacement-based formulations and previously proposed hybrid-mixed formulations. Displacement fields are recovered a posteriori by integrating the kinematic compatibility relations, producing globally C0 -continuous fields that satisfy all prescribed kinematic boundary conditions. Nonlinear equilibrium paths are traced using an arc-length strategy with a linear extrapolation predictor, and critical points are identified through the determinant of a Schur-complement-based equivalent stiffness matrix that emerges naturally from the formulation. Numerical examples demonstrate the accuracy, convergence, and robustness of the proposed approach, including verification against analytical solutions under pure bending, assessment of shear-locking performance, and the simulation of complex nonlinear responses involving snap-through, snap-back, and symmetry-breaking bifurcation phenomena.
Descrição
Palavras-chave
Beam and frame structures Geometrically exact beam theory Large displacements and rotations Mixed finite element formulation Shear locking Stability analysis
Contexto Educativo
Citação
Santos, H.A.F.A. A new, simple, and effective variationally consistent mixed finite element formulation for the geometrically exact planar analysis of beams and frames. Computational Mechanics (2026). https://doi.org/10.1007/s00466-026-02855-x
Editora
Springer