Transverse Compression of a Thin Inhomogeneous Elastic Layer

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.