About numerical realization of the method of subsequent parameters perturbation for calculating a stress-strain state of shallow shells

The paper investigates a class of nonlinear dynamic shell models, which non-linearity reflects Gaussian curvature of a surface; in the case when loads are smaller than critical ones in every point in time. Moreover, every unknown function from the system of equations, can be uniquely identified through the deflection function. Domain that is defined by the middle shell surface is bounded with piecewise smooth boundary. Such models as Kirchhoff–Love model (that specify Tymoshenko model, defined both in transferences and mixed forma), a model that reflects the bond between deformation fields and temperature and others can represent that equation class.
The method of subsequent parameters perturbation developed by professor V. Petrov in 1970s is used as a numerical method for such models. This method brings the solution of nonlinear equations to the solution of a sequence of linear equations. The paper discusses problems connected with the realization of this method. It is known, that method of V. Petrov converges slowly. That is why questions of convergence improvement are examined. The usage of variation methods for solving systems of linear equations requires defined convergence speed and orthogonal system of functions that satisfies the boundary conditions. These questions are investigated in the paper as well.