International audienceThe corotational method is an attractive approach to derive non-linear finite beam elements. In a number of papers, this method was employed to investigate the non-linear dynamic analysis of 2D beams. However, most of the approaches found in the literature adopted either a lumped mass matrix or linear local interpolations to derive the inertia terms (which gives the classical linear and constant Timoshenko mass matrix), although local cubic interpolations were used to derive the elastic force vector and the tangent stiffness matrix. In this paper, a new corotational formulation for dynamic nonlinear analysis is presented. Cubic interpolations are used to derive both the inertia and elastic terms. Numerical examples show that the proposed approach is more efficient than using lumped or Timoshenko mass matrices

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Abstract. 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. Several numerical examples are considered to assess the performance of the new formulation against the one suggested by . 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.

Abstract. The paper investigates the contribution of the warping deformations and the shear center location on the dynamic response of 3D thin-walled beams obtained with an original consistent co-rotational formulation developed by the authors. Consistency of the formulation is ensured by employing the same kinematic assumptions to derive both the static and dynamic terms. Hence, the element has seven degrees of freedom at each node and cubic shape functions are used to interpolate local transversal displacements and axial rotations. Accounting for warping deformations and the position of the shear center produces additional terms in the expressions of the inertia force vector and the tangent dynamic matrix. The performance of the present formulation is assessed by comparing its predictions against 3D-solid FE solutions.

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