A 3D mixed frame element with multi-axial coupling for thin-walled structures with damage
A 3D mixed beam finite element is presented, modeling the warping of the cross-sections as an independent kinematic field. The beam formulation is derived on the basis of the Hu-Washizu variational principle, expressed as function of four independent fields: the standard displacements, strains and...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Gruppo Italiano Frattura
2014-07-01
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| Series: | Fracture and Structural Integrity |
| Subjects: | |
| Online Access: | http://www.gruppofrattura.it/pdf/rivista/numero29/numero_29_art_16.pdf |
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| Summary: | A 3D mixed beam finite element is presented, modeling the warping of the cross-sections as an
independent kinematic field. The beam formulation is derived on the basis of the Hu-Washizu variational
principle, expressed as function of four independent fields: the standard displacements, strains and stresses and
the additional warping displacement. This is interpolated along the beam axis and on the cross-section, by
placing on it a regular grid of interpolation points and adopting Lagrange polynomials. The warping degrees of
freedom defined at the cross-section interpolation points are condensed, thus preserving the element matrix and
vector sizes. A fiber discretization of the cross-sections is adopted. The constitutive relationship at the midpoint
of each fiber is based on an isotropic damage model for brittle-like materials, distinguishing between the damage
variables in tension and in compression to properly describe the unilateral effect. An efficient algorithm is
formulated for the element state determination, based on a consistent linearization of the governing equations.
A simple numerical application on a cantilever beam with torsion in the linear elastic range is presented and two
torsion tests on plain concrete beams are performed, by comparing the numerical results with the experimental
outcomes. |
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| ISSN: | 1971-8993 1971-8993 |