Geometrically non-linear and elastoplastic three-dimensional shear flexible beam element of von-Mises-type hardening material

Abstract

A three-dimensional elastoplastic beam element being capable of incorporating large displacement and large rotation is developed and examined. Elastoplastic constitutive equations are applied to the beam element based upon the assumption of small deformational strain leading to a material formulation which is completely objective for the application of stress update procedures. The continuum-type equations of plastic model of J(2) mixed hardening are transformed into the beam equations by satisfying beam hypotheses. An effective stress update algorithm is proposed to integrate elastoplastic rate equations by means of the so-called multistep method which is a method of successive control of residuals on yield surfaces. It avoids severe divergence when the displacement increments become large which is usual for the continuation methods. Material tangent stiffness matrix is derived by using consistent elastoplastic modulus resulting from the integration algorithm and is combined with geometric tangent stiffness matrix. Different from other elements, the present element is shear flexible and can satisfy the plasticity condition in a pointwise fashion. A great number of numerical examples are analysed and compared with the literature. The proposed beam element is verified to be not only quite accurate but also very effective for the analyses of pre-buckling and large deflection collapse of spatial framed structures.