# INFORMATION TECHNOLOGIES

**Computer simulation of unsteady elastic stress waves in a console and a ten-storey building under fundamental influence in the form of a Heaviside function**

1,2Vyacheslav K. Musayev
1Moscow State University of Civil Engineering, https://mgsu.ru/

Moscow 129337, Russian Federation

2Russian University of Transport, https://www.miit.ru/

Moscow 127994, Russian Federation

*E-mail: musayev-vk@yandex.ru*
*Received February 14, 2022, peer-reviewed February 21, 2022, accepted March 1, 2022*

**Abstract:**: The aim of the work is to consider the problems of numerical simulation of seismic safety of a console and a ten-storey building with a base in the form of an elastic half-plane under non-stationary wave influences. Modeling of tasks of the transition period is an actual fundamental and applied scientific task. Methodology. To solve a two-dimensional plane dynamic problem of elasticity theory with initial and boundary conditions, the finite element method in displacements is used. Based on the finite element method in displacements, an algorithm and a set of programs have been developed for solving linear planar two-dimensional problems that allow solving problems with non-stationary wave effects on complex systems. The algorithmic language Fortran-90 was used in the development of the software package. Результаты. Results. The problem of the effect of a plane longitudinal wave in an elastic half-plane in the form of four trapezoids and in the form of two half-periods of a sinusoid is considered to assess the physical reliability and mathematical accuracy. A system of equations consisting of 8016008 unknowns is solved. The problem of the effect of a plane longitudinal elastic wave in the form of a Heaviside function on a console with a base (the ratio of width to height is one to ten) is considered. A system of equations consisting of 16016084 unknowns is solved. The problem of the effect of a plane longitudinal elastic wave in the form of a Heaviside function on a ten-storey building with a base in the form of a half-plane is considered. A system of equations consisting of 16202276 unknowns is solved. Contour stresses and components of the stress tensor are obtained in the characteristic areas of the problem under study. Based on the conducted research, the following conclusions can be drawn. Elastic contour stress on the sides of the console and a ten-story building are almost a mirror image of each other, that is, antisymmetric. The console and supporting structures of the building work like a beam during seismic action, that is, if there are tensile stresses on one side, then compressive stresses on the other. Bending waves mainly prevail on the contours of the console and supporting structures of the building under seismic influence.

*Keywords*: mathematical modeling, wave theory of seismic safety, seismic impact, fundamental impact, Heaviside function, verification of the numerical method, console, ten-storey building, elastic half-plane, contour stress, bending waves

UDC 539.3

*RENSIT*, 2022, 14(2):187-196e.

**DOI: 10.17725/rensit.2022.14.187. **

*Full-text electronic version of this article - web site http://en.rensit.ru/vypuski/article/444/14(2)187-196e.pdf*