A consistent 3D corotational beam element for nonlinear dynamic analysis of flexible structures

•The paper proposes a consistent nonlinear dynamic formulation for 3D beam elements.•The kinematical corotational description is used to derive both internal and inertia terms.•Cubic interpolation functions are used to formulate the local deformational terms.•The formulation is more efficient than the classical one proposed by Simo and Vu-Quoc.

The purpose of the paper is to present a corotational beam element for the nonlinear dynamic analysis of 3D flexible frames. The novelty of the formulation lies in the use of the corotational framework (i.e., the decomposition into rigid body motion and pure deformation) to derive not only the internal force vector and the tangent stiffness matrix but also the inertia force vector and the tangent dynamic matrix. As a consequence, cubic interpolations are adopted to formulate both inertia and internal local terms. In the derivation of the dynamic terms, an approximation for the local rotations is introduced and a concise expression for the global inertia force vector is obtained. To enhance the efficiency of the iterative procedure, an approximate expression of the tangent dynamic matrix is adopted. Four numerical examples are considered to assess the performance of the new formulation against the one suggested by Simo and Vu-Quoc (1988) [48]. It was observed that the proposed formulation proves to combine accuracy with efficiency. In particular, the present approach achieves the same level of accuracy as the formulation of Simo and Vu-Quoc but with a significantly smaller number of elements.