The Use of a Modified Discrete Continuation Method to Solve Nonlinear Problems in the Reforming of Thin-Walled Shells

An algorithm for the discrete continuation method for solving systems of nonlinear algebraic equations that describe the steady-state behavior of thin-walled structures, and have limit and bifurcation points on the path of their solutions, is presented. It is structured for joint use with the continuous extension method in order to reduce the error of numerical procedures of the latter. It is based on the transformation of the space of arguments for solving systems of nonlinear algebraic equations, which is constructed using eigenvectors of the Jacobi matrix, and its computational basis is the Newton-Raphson method implemented in the extended space of arguments of the solution taking into account the idea of their equality.