Contact between shear-deformable beams with elliptical cross sections

• Published in: Acta mechanica Vol. 231; no. 1; pp. 273 - 291
• Main Authors: Magliulo, M., Zilian, A., Beex, L. A. A.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 2020; Springer; Springer Nature B.V
• Subjects: Classical and Continuum Physics; Constituents; Control; Cross-sections; Deformation; Dynamical Systems; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Formability; Heat and Mass Transfer; Kinematics; Original Paper; Solid Mechanics; Theoretical and Applied Mechanics; Vibration
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-019-02520-w

Slender constituents are present in many structures and materials. In associated mechanical models, each slender constituent is often described as a beam. Contact between beams is essential to incorporate in mechanical models, but associated contact frameworks are only demonstrated to work for beams with circular cross sections. Only two studies have shown the ability to treat contact between beams with elliptical cross sections, but those frameworks are limited to point-wise contact, which narrows their applicability. This contribution presents initial results of a framework for shear-deformable beams with elliptical cross sections if contact occurs along a line or at an area (instead of at a point). This is achieved by integrating a penalty potential over one of the beams’ surfaces. Simo–Reissner geometrically exact beam elements are employed to discretize each beam. As the surface of an assembly of such beam elements is discontinuous, a smoothed surface is introduced to formulate the contact kinematics. This enables the treatment of contact for large sliding displacements and substantial deformations.