The solution method and its accuracy for a nonlinear Timoshenko axisymmetric shell model

The boundary value problem of the axisymmetric displacement of a Timoshenko (cylindrical) shell in static regime was considered. From the given nonlinear system of ordinary differential equations with respect to the displacement functions u, w and ψ, using the Green functions, we obtain an integro-differential equation for the function w. This equation, together with the Dirichlet boundary condition, forms the boundary value problem. To obtain an approximate solution of the problem for w we apply the method that includes the Galerkin method and the Jacobi–Cardano iteration. Obtained values of w and of its error estimate are used for constructing the approximations for other displacement functions u and ψ and for estimation of their errors. The results of the numerical experiment are given.