A 3D mixed frame element with multi-axial coupling for thin-walled structures with damage (Fracture and Structural Integrity, 2014)
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 damagevariables in tension and in compression to properly describe the unilateral effect. An efficient algorithm isformulated 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.
Keywords: Mixed beam formulation