Transverse Compression of a Thin Inhomogeneous Elastic Layer

Ahmed S. M. Alzaidi, Julius Kaplunov, Barbara Zupančič and Anatolij Nikonov ()
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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

Mathematics, 2024, vol. 12, issue 16, 1-11

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.

Keywords: thin elastic layer; asymptotic; transverse compression; inhomogeneity; functionally graded materials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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