Mathematical modeling of structural elements destruction under dynamic load

The development of modern industry puts forward a responsible and complex task of protecting the population, service personnel and the environment from accidents. The analysis of possible deviations from normal operating conditions in these industries and a thorough study of the possible development of various emergency situations that lead to dynamic effects on structures and finding conditions for the destruction of structural elements is of paramount importance. The article proposes a mathematical method for finding the conditions of destruction of structural elements by dynamic loading. To solve dynamic problems, a variational approach is used, based on the construction of a functional for calculating the power of elastic deformation taking into account the power of inertia forces, in the context of using modern software systems based on the finite element method. As an example, the problem of computer modeling of the dynamic load located above the center of the reinforced concrete slab, which allows to determine the stress-strain state of the simplest elements of building structures of plates, is considered. All calculations were performed in ANSYSLS-DYNA environment. The results are obtained in the form of graphs of strain rates and stress fields. The obtained results are compared with the analytical solution of a similar problem presented in the work of G.T. Volodin.