Akademik Məlumat İdarəetmə Sistemi
Thin-Walled Structures, vol.214, 2025 (SCI-Expanded)
In this study, the axisymmetric problem of functionally graded (FG) transversely isotropic spheres in the radial direction, which do not contain 0 and Pi poles, is investigated within the framework of 3D-elasticity theory. In this study, firstly, the elasticity theory of spheres made of homogeneous materials extended to the elasticity theory of functionally graded transversely isotropic (FGTI) spheres. Arbitrary stresses are applied to the slots that keep the hollow sphere, whose lateral surface is assumed to be fixed, in balance. Asymptotic formulas are obtained to calculate the displacements and stresses of FGTI hollow spheres for the first time. The solution of the problem consists of solutions belonging to the nature of the boundary layer localized in the slots (conical sections) inside the sphere, which is equivalent to the Saint-Venant boundary effect for FG plates. Unlike the FG isotropic sphere, weak transitional boundary layer solutions that spread far from the conical sections for FGTI spheres emerge. In addition, an asymptotic solution to the torsion problem for thin FGTI spheres is presented for the first time. The realized asymptotic solutions can be a criterion for determining the fields of application of the existing applied theories of FGTI spheres. Based on the proposed solutions, more accurate new applied theories for heterogeneous transversely isotropic spherical shells can be constructed. Finally, the changes in displacements and stresses compared to the homogeneous case are analyzed in detail when the modulus of elasticity changes linearly and inversely proportional to the radius.