COMPLETE CLOSED-FORM SOLUTION FOR PRESSURIZED HETEROGENEOUS THICK SPHERICAL SHELLS

Abstract

On the basis of plane elasticity theory (PET), the governing equations for axisymmetric thick spherical shells made of nonhomogeneous functionally graded materials (FGMs) subjected to internal and external pressure in general case are derived. It is assumed that the modulus of elasticity varies nonlinearly in the radial direction, and the Poisson’s ratio is constant. The analytical solution of the equations for real, double and complex roots are obtained. The radial stress, meridional stress and radial displacement distributions depending on an inhomogeneity constant are compared with those of the homogeneous case as well as with the solution using finite element method (FEM) and presented in the form of graphs. The obtained result shows that the property of FGMs has a significant influence to the stress distribution along the radial direction. Results are useful for engineers to design a sphere made of FGMs.

DOI: http://dx.doi.org/10.5755/j01.mech.18.5.2702