Review article

The paper presents the development of methods and models for calculating thin-walled shells for new (in the context of the approach under consideration) types of dynamic effects important for ensuring safe operation of structures. The author considers the load linearly dependent on time, periodic action and explosive load. The geometrically nonlinear mathematical model is modified, taking into account the orthotropy of the material and transverse shears. The computational algorithm is based on using the L. V. Kantorovich method and the Rosenbrock method for solving a rigid system of ordinary differential equations. The Maple analytical computing environment is used. The applicability of the proposed approach is shown by the example of calculating a shallow shell of double curvature under different loading options.