Corotational mixed finite element formulation for thin-walled beams with generic cross-section

International audienceThe corotational technique is adopted here for the analysis of three-dimensional beams. The technique exploits the technology that applies to a two-noded element, a coordinate system which continuously translates and rotates with the element. In this way, the rigid body motion is separated out from the deformational motion. In this paper, a mixed formulation are adopted for the derivation of the local element tangent stiffness matrix and nodal forces. The mixed finite element formulation is based on an incremental form of the two-field Hellinger-Reissner variational principle to permit elasto-plastic material behavior. The local beam kinematics is based on a low-order nonlinear strain expression using Bernoulli assumption. The present formulation captures both the Saint-Venant and warping torsional effects of thin-walled open cross-sections. Shape functions that satisfy the nonlinear local equilibrium equations are selected for the interpolation of the stress resultants. In particular, for the torsional forces and the twist rotation degree of freedom, a family of hyperbolic interpolation functions is adopted in lieu of conventional polynomials. Governing equations are expressed in a weak form, and the constitutive equations are enforced at each integration cross-section along the element length. A consistent state determination algorithm is proposed. This local element, together with the corotational framework, can be used to analyze the nonlinear buckling and postbuckling of thin-walled beams with generic cross-section. The present corotational mixed element solution is compared against the results obtained from a corotational displacement-based model having the same beam kinematics and corotational framework. The superiority of the mixed formulation is clearly demonstrated. (C) 2010 Elsevier B.V. All rights reserved

Three-dimensional formulation of a mixed corotational thin-walled beam element incorporating shear and warping deformation

International audienceThis paper presents a corotational formulation of a three-dimensional elasto-plastic mixed beam element that can undergo large displacements and rotations. The corotational approach applies to a two-noded element a coordinate system which continuously translates and rotates with the element. In this way, the rigid body motion is separated out from the deformational motion. In this paper, a mixed formulation is adopted for the derivation of the local element tangent stiffness matrix and nodal forces based on a two-field Hellinger-Reissner variational principle. The local beam kinematics is based on a low-order nonlinear strain expression using Timoshenko assumption. The warping effects are characterized by adopting Benscoter theory that describes the warping degree of freedom by an independent function. Shape functions that satisfy the nonlinear local equilibrium equations are selected for the interpolation of the stress resultants. This local element, together with the corotational framework, can be used to analyze the nonlinear buckling and postbuckling of thin-walled beams with generic cross-section. The mixed formulation solution is compared against the results obtained from a corotational displacement-based formulation having the same beam kinematics. The superiority of the mixed formulation is clearly demonstrated. (C) 2010 Elsevier Ltd. All rights reserved