Magneto-thermal-mechanical analysis of functionally graded thick-walled spherical vessels

The analytical solutions of the thermal distribution, mechanical distribution of displacement and stress for a rotating functionally graded material (FGM) thick-walled spherical pressure vessel are obtained under a uniform constant magnetic field. Here, the vessel is subjected to spherically symmetrical thermal and mechanical loads, and the FGM properties change as the power function along with the thickness of the pressure vessel in this paper. On the basis of the dynamic equation with the Lorentz force effect, the analytical solutions of various physical fields are obtained, where the finite difference method (FDM) is also given for this problem. The four simplified problems are solved as the special cases of our present analytical expressions. The present theory is verified by the comparison with the solutions in the existing works or the numerical results from FDM. In addition, the effects of different physical fields such as the mechanical, magnetic, and thermal fields on the coupling response of FGM spherical vessels are studied in detail. There are significant coupling effects on the distributions of displacement and stresses. The FGM thick-walled spherical vessel designed with suitable FGM parameters can realize the optimal regulation of displacement and stresses distribution.