The present paper develops a non-linear beam element for analysis of elastoplastic frames under large displacements. The finite element formulations are derived by using the co-rotational approach and expression of the virtual work. The Gauss quadrature is employed for numerically computing the element tangent stiffness matrix and internal force vector. A bilinear stress-strain relationship with isotropic hardening is adopted to update the stress. | Vietnam J ournal of Mechanics, VAST, Vol. 26, 2004, No. 1 (39 - 54) BEAM ELEMENT FOR LARGE DISPLACEMENT ANALYSIS OF ELASTO-PLASTIC FRAMES NGUYEN DINH KIEN 1 AND D o Quoc QuANG 2 1 2 Institute of Mechanics Vietnamese Academy of Science and Technology Research Institute of Technology for Machin ery, Ministry of Industry ABSTRA CT. The present paper develops a non-linear beam element for analysis of elastoplastic frames under large displacements. The finite element formulations are derived by using the co-rotational approach and expression of the virtual work. The Gauss quadrature is employed for numerically computing the element tangent stiffness matrix and internal force vector. A bilinear stress-strain relationship with isotropic hardening is adopted to update the stress. The arc-length technique based on the Newton-Raphson iterative method is employed to compute the equilibrium paths. A number of numerical examples is employed to assess the performance of the developed element. The effects of plastic action on t he large displacement behavior of the structures as well as the expansion of plastic zones in the loading process are discussed. 1 Introduction In the previous work [1, 2], the authors investigated some beam elements for assessing the behavior of elastic frames under large displacements. The finite element formulations in the work have been developed by using the co-rotational approach, in which an element attached coordinate system which continuously rotates and moves during the element deformation process was employed. The approach allowed to derive the finite element formulations in a local system, and then transfer them to a global one with the aid of the transformation matrices . In add ition, the stress-strain relationship was assumed to be linear, and this assumption enabled to derive the element formulations from the expression of strain energy. As consequences , t he explicit forms of the element tangent stiffness matrix and internal force
