On stresses and deformations in anisotropic toriodal shells subjected to uniform internal pressure

An analysis of a thin toroidal shell of circular cross section, constructed form a plane anisotropic material and subjected to uniform internal pressure, is conducted with the use of linear bending theory. The analysis leads to a set of two simultaneous, linear, second-order differential equations with variable coefficients, the solution to which yields relationships describing the structural behavior of the middle surface of the shell. A closed form solution, using the method of asymptotic integration, is obtained for the differential equations for an orthotropic material. Engineering formulas for the stress resultants, stress couples, and deformations, applicable to an orthotropic and isotropic material, are presented