A hybrid shell-beam element for straight thin-walled tubular structures

Abstract

A novel beam model is proposed in order to consider deformations of its cross-section in the context of straight thin-walled tubes. For this purpose, the straight beam kinematics is enriched by addition of orthogonal shell-type displacement field of the tube section. Linear strain in terms of displacement is considered in conjunction with the non-linear coupling between local deformation of the section and its global rotation. Both Euler–Bernoulli and Love-Kirchhoff hypotheses for beam and shell kinematics, respectively, are adopted as well as the thin-walled assumption. First-order shear deformation for the radial variable and Fourier expansion in terms of the circumferential variable are also considered for the mid-surface displacement field. Then, the stress tensor is obtained under plane stress conditions. The virtual power principle is finally used to obtain the equations of motion satisfied by the corresponding generalized forces. Afterwards, an explicit updated Lagrangian Finite-Element approach using a lumped mass matrix is proposed for solving the tube governing equations and the stability condition of the time integration is given. Test-cases are then chosen to assess the present tube finite-element. Both static and dynamic problems are considered. First, the proposed model is compared to analytical solutions. Finally, a tube subjected to a distributed patch loading is studied. The influence of the number of Fourier modes, of warping and coupling terms is examined. The proposed model makes it possible to retrieve classical shell solution of the cross-section deformation with significant computational savings.