Numerical solution of the problem of deformation of elastic solids under pulsed loading

I. O. Bogulskii^ab, Yu. M. Volchkov<sup>cd

a</sup> Siberian Federal University, 660041, Krasnoyarsk, Russia
^b Krasnoyarsk State Agrarian University, 660049, Krasnoyarsk, Russia
^c Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
^d Novosibirsk State University, 630090, Novosibirsk, Russia

Abstract: Three methods of approximation of lower non-differential terms in equations of dynamic problems of mechanics of deformable solids are studied with the use of explicit algorithms of the numerical solution based on several local approximations of each of the sought functions by linear polynomials. Additional equations based on the energy conservation law are formulated in the course of algorithm construction. The properties (dissipativity, monotonicity, and stability) of the proposed schemes are studied. Results of the numerical solution of the problem of deformation of an elastic plate with constant shear strains over the plate thickness (Timoshenko model) are presented. Results of the numerical solution of the problem of deformation of an elastic disk under pulsed loading are compared with the analytical solution of this problem.

Keywords: numerical methods, dissipation constants, pulsed loading, elastic deformable solids.

UDC: 539.3

Received: 02.03.2020
Revised: 02.03.2020
Accepted: 02.03.2020

DOI: 10.15372/PMTF20200415

 English version: Journal of Applied Mechanics and Technical Physics, 2020, 61:4, 611–622