Nonclassical Shell Theories for the Analysis of Transversally Isotropic Spherical and Cylindrical Layers under Normal Pressure

In the present paper, the stress-strain states of transversally isotropic spherical and cylindrical layers under normal pressure have been studied. These structures can be used as basic models for the eyeball or blood vessels. Solutions have been obtained using the exact 3D theory of elasticity and two approximate theories for orthotropic plates: the theory of shells of moderate thickness developed by Paliya–Spiro (PS) and the refined theory developed by Rodinova–Titaev–Chernykh (RTC). Expansions of the 3D exact solutions in powers of a small parameter, which is equal to the relative thickness of he spherical or cylindrical layers, are compared with the solutions obtained with the PS and RTC shell theories. Both nonclassical theories correctly produce the first two terms of asymptotic expansions of the 3D solution for displacements.