Non-conventional non-linear two-node hybrid stress-strain curved beam elements

Abstract

This paper presents a family of two-node hybrid stress–strain curved beam elements with four displacement degrees of freedom (dof) per node for the finite deformation 2D Timoshenko beam theory, which can be readily generalized on the two-node curved beam elements with six displacement dof for the 3D beam theory. The developed formulation is based on the principally new non-linear strain–displacement relationships that are objective, i.e., invariant under arbitrarily large rigid-body motions. To avoid shear and membrane locking and have no spurious zero energy modes, the assumed stress resultant and strain fields are invoked. In order to circumvent thickness locking, the modified material stiffness matrices corresponding to the plane stress state are employed. The fundamental unknowns consist of four displacements and five strains of the face lines of the beam, and five stress resultants. The element characteristic arrays are obtained by using the Hu-Washizu variational principle. To demonstrate the efficiency and accuracy of this formulation and to compare its performance with other non-linear finite element models reported in the literature, extensive numerical studies are presented.