Analytical evaluation of the elastic stresses in a multilayer spherical pressure vessel

An explicit-form solution is constructed for a problem on elastic deformation of a multilayer spherical vessel due to uniform internal pressure. The vessel is assembled of perfectly connected elastic layers whose material properties may arbitrarily vary across their thickness. The solution is constructed through the use of the single solid approach along with the modified scheme of the direct integration method which allow for the consideration of the multilayer vessel as a composite sphere with piecewise-variable profiles of the material properties. As a result, the original problem is reduced to solving a governing integral equation of the second kind whose solution is constructed in the form of the explicit dependence on the internal pressure. The solution is verified by the comparison with exact solutions derived by making use the method of tailored solutions for specific benchmark problems. By comparing our with the one for a functionally-graded sphere, whose material properties are evaluated through the use of the micromodular homogenization technique, the specific features of the circumferential stress are analyzed.