Algorithmization of solving dynamic edge problems of the theory of flexible rectangular plates

In this paper, a computational algorithm is developed on the basis of the finite difference method for solving dynamic edge problems of the theory of flexible shells with account for shears and rotary inertia.
Dynamic calculations of flexible plates is used in designing hulls of ships, aircraft, missiles, and other technical objects, which, along with sufficient strength, should have the least weight ensured by the use of lightweight plates and by reducing the margin of safety. The problem of developing an automated system for solving problems of the theory of elasticity and plasticity was first raised in the monograph by V.K. Kabulov. This work reveals the main problems of algorithmization and indicates approaches for their machine solution.
In accordance with the analyzed problems, which arise during automated calculations of thin-walled elements of mechanical engineering structures, it is reasonable to use a nonlinear dynamic computational scheme for a flexible homogeneous isotropic linear elastic shell of arbitrary shape and to take into account the effect of both shears and rotary inertia when describing the motion of the shell. Such a model allows one to apply a sufficiently flexible and fast-acting scheme to calculate a wide class of dynamic processes taking place within the plates and shells of different shapes which are not over-limited in thickness and serve as significant parts of mechanical engineering elements.
A number of dynamic differential equations of plate motion have been developed and tested. Obviously, there is no need to build other algorithms to calculate flat plates when developing an automated computational system.