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Transverse Compression of a Thin Inhomogeneous Elastic Layer

Author

Listed:
  • Ahmed S. M. Alzaidi

    (Department of Mathematics and Statistics, College of Science, Taif University, Taif 21944, Saudi Arabia)

  • Julius Kaplunov

    (School of Computing and Mathematics, Keele University, Newcastle ST5 5BG, UK)

  • Barbara Zupančič

    (Theory Department, National Institute of Chemistry, 1000 Ljubljana, Slovenia)

  • Anatolij Nikonov

    (Faculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia)

Abstract

A 3D problem in linear elasticity is considered for a thin inhomogeneous layer subject to transverse compression. For the first time, the effect of arbitrary vertical inhomogeneity is elucidated. Two sets of boundary conditions along the faces of the layer are adapted for modelling transverse compression. Robust asymptotic formulae involving repeated integrals across the thickness are derived for displacements and stresses. As an illustration, numerical results are presented for the elastic moduli having a transverse parabolic variation. The obtained results have a potential to be implemented in modern technology, including manufacturing and design of functionally graded materials.

Suggested Citation

  • Ahmed S. M. Alzaidi & Julius Kaplunov & Barbara Zupančič & Anatolij Nikonov, 2024. "Transverse Compression of a Thin Inhomogeneous Elastic Layer," Mathematics, MDPI, vol. 12(16), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2502-:d:1455605
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