An elasticity solution for a transversely isotropic material containing a spherical shell under axisymmetric loading
A three-dimensional elasticity solution is obtained for a transversely isotropic solid containing an isotropic spherical shell. The shell is assumed to behave as a membrane which is perfectly bonded to the surrounding medium. The applied loading may consist of any arbitrary axisymmetric traction distribution applied to the inner shell surface and/or at infinity. The solution method is based on the superposition of two fundamental solutions: those corresponding to (1) the spherical cavity problem for transverse isotropy, and (2) the spherical membrane shell problem. Each solution is expressed in the form of Legendre series, and the displacement continuity conditions are then utilized to generate an infinite system of linear algebraic equations in terms of the unknown series coefficients. The solution of this system is obtained by means of an explicit limiting procedure. Numerical results generated by the solution provide the opportunity to investigate the influence of geometric parameters, material constants, and loading type on the displacements and stresses at the interface of the shell and surrounding medium, as well as the internal shell forces. In general, the presence of a shell of intermediate stiffness is preferable in reducing the maximum stress concentration for mildly anisotropic materials (e.g., magnesium and zinc) and isotropic materials under the loading at infinity. For more highly anisotropic materials such as graphite, the stiffest shell was found to minimize the stress concentration.
Jiun-Yih John Wang,
"An elasticity solution for a transversely isotropic material containing a spherical shell under axisymmetric loading"
(January 1, 1991).
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