Free vibration analysis of thin to thick straight or curved beams by a solid-3D beam finite element method: Fid-Bau Portal

Free vibration analysis of thin to thick straight or curved beams by a solid-3D beam finite element method

Wei, Guoqiang / Lardeur, Pascal / Druesne, Frédéric

Abstract A solid-3D beam finite element method is presented for the vibration analysis of thin to thick beam-like structures. This method is efficient for a spatial beam and considers all mechanical effects: membrane, bending and torsion. The structure is discretized with solid elements and contains several elements throughout the cross-section. Displacement fields of first-order or higher-order beam theories are met by directly applying kinematic relations on the solid finite element model, throughout the cross-section. This leads to a set of linear equations applied at slave nodes. Only the master nodes are kept in the final model, resulting in a model size reduction. The effectiveness of this method is demonstrated through two numerical examples, including a straight and a curved beam. The modal shapes and natural frequencies obtained by the proposed method are compared with the complete solid model and classical beam model. The size of these solid-beam models is slightly larger than that of an approach with classical beam element.

Highlights • A new solid-beam finite element method based on applications of 3D first-order or higher-order beam theories to standard solid finite element models is presented. • Kinematic relations are imposed at nodes to meet displacement fields throughout the cross-section beam. • The method works for a spatial beam and considers all mechanical effects: membrane, bending, transverse shear and torsion. • The effectiveness of this method is demonstrated through the free vibration analysis of a thin or thick straight beam and a thin or thick curved one. • The results presented show that the solid-3D beam finite element method proposed is efficient in terms of quality of results and model size.