Complete systems method for linear and nonlinear problems of shallow shells theory

摘要

The approach to solving two-dimensional nonlinear (linear) boundary-value problems for shallow shells using the complete systems and quasilinearization Newton-Kantorovich-Raphson methods is developed. With the complete systems method in linear case, the original two-dimensional boundary-value problem is reduced to thise system of two interconnected one-dimensional problems, which is solved iteratively using the method similar to the Libman-Gauss-Seidel successive replacement method. The rational combination of the qusi-linearization method and complete systems method makes it possible to construct a single generalized iterative process of solving the problem as a whole in nonlinear case. For the process, typical is rapid convergence (the number of iterations within the limits of one order) and a few number of approximating functions in the accepted presentation form (2 - 4).Possibilities of the approach proposed are illustrated by examples of solving mean-bending problems for shallow shells with rectangular planform.