Small symmetrical deformation of thin torus with circular cross-section

By introducing a variable transformation ?=12(sin?+1), complex-form ordinary differential equation (ODE) for the small symmetrical deformation of an elastic torus is successfully transformed into well-known Heun’s ODE, whose exact solution obtained in terms functions. To overcome computational difficulties ODE dealing with boundary conditions, real-form system proposed. A general code numerical written by using Maple. Some studies are carried out and verified both finite element analysis H. Reissner’s formulation. Our investigations show that stress response sensitive to radius ratio, suggest should be done bending theory shell. Maple provided as essential part this paper.