Three-dimensional formulation of a mixed corotational thin-walled beam element incorporating shear and warping deformation
2011 (English)In: Thin-walled structures, ISSN 0263-8231, E-ISSN 1879-3223, Vol. 49, no 4, 523-533 p.Article in journal (Refereed) Published
This 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.
Place, publisher, year, edition, pages
Elsevier, 2011. Vol. 49, no 4, 523-533 p.
Geometrically nonlinear beams, Corotational formulation, Three-dimensional mixed finite element analysis, Elasto-plastic material behavior, Two-field Hellinger-Reissner functional, Timoshenko beam theory, Benscoter torsion theory
IdentifiersURN: urn:nbn:se:kth:diva-32224DOI: 10.1016/j.tws.2010.12.002ISI: 000288478800007ScopusID: 2-s2.0-79951670332OAI: oai:DiVA.org:kth-32224DiVA: diva2:420319
QC 201106012011-06-012011-04-112016-05-02Bibliographically approved