Generalized Method of Finite Integral Transformations in Linear and Nonlinear Static Problems for Shallow Shells

We propose an approach to solving two-dimensional linear and nonlinear boundary-value problems of statics for shallow shells based on the generalized method finite integral transformations Newton– Kantorovich–Raphson linearization. In case, application is reduced construction two with respect different variables in analyzed domain under assumption that kernels one transformation are transforms second transformation, vice versa. To solve obtained system one-dimensional problems, we use iterative procedure, which analog Libman– Gauss–Seidel procedure algebra. basis a rational combination Newton–Kantorovich–Raphson linearization transformations, construct single process combines types iterations, namely, problem (Newton–Kantorovich–Raphson method) separate linearized (Libman–Gauss–Seidel method). This converges sufficiently rapidly (the number iterations within limits order magnitude) gives stationary solution input small (3–5) (kernels) inverse transformation. present examples verification proposed study stability various conditions fastening boundary contour.