Convergence of the Method of Consecutive Approximations in Geometrically Nonlinear Problems.

On the example of the problem of considerable sags of a flat curvilinear beam - which has an exact solution - the possibility of substantiating the convergence of the method of consecutive approximations by means of Cauchy majorants is investigated. Practical usefulness of such a proof is considered. It is shown that by using majorant relations it is possible to prove the convergence of consecutive approximations and to obtain evaluations of the proximity of the n-th approximation to an exact solution.