Transverse compression of a thin elastic disc

Alzaidi, Ahmed S. M.; Kaplunov, Julius; Nikonov, Anatolij; Zupančič, Barbara

Abstract

The mathematical formulations for transverse compression of a thin elastic disc are considered, including various boundary conditions along the faces of the disc. The mixed boundary conditions corresponding to the loading by normal stresses in absence of sliding are studied in detail. These conditions support an explicit solution in a Fourier series for the boundary layers localised near the edge of the disc and also do not assume making use of the Saint-Venant principle underlying the traditional asymptotic theory for thin elastic structures. As an example, an axisymmetric problem is studied. Along with the leading order solution for a plane boundary layer, a two-term outer expansion is derived. The latter is expressed through the derivatives of the prescribed stresses. Generalisations of the developed approach are addressed.

Citation

Alzaidi, A. S. M., Kaplunov, J., Nikonov, A., & Zupančič, B. (2024). Transverse compression of a thin elastic disc. Zeitschrift für angewandte Mathematik und Physik, 75(3), Article 116. https://doi.org/10.1007/s00033-024-02238-3

• Journal Article Type: Article
• Acceptance Date: Mar 17, 2024
• Online Publication Date: May 23, 2024
• Publication Date: Jun 1, 2024
• Deposit Date: May 28, 2024
• Publicly Available Date: May 28, 2024
• Journal: Zeitschrift für angewandte Mathematik und Physik
• Print ISSN: 0044-2275
• Publisher: Birkhäuser Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 75
• Issue: 3
• Article Number: 116
• DOI: https://doi.org/10.1007/s00033-024-02238-3
• Keywords: Compression, Mixed conditions, Thin elastic disc, Boundary layer, Asymptotic, 74-10
• Public URL: https://keele-repository.worktribe.com/output/833070
• Publisher URL: https://link.springer.com/article/10.1007/s00033-024-02238-3