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Journal of Applied Mechanics and Technical Physics

2020 year, number 4

Numerical Solution of the Problem of Deformation of Elastic Solids under Pulsed Loading

I. O. Bogulskii1,2, Yu. M. Volchkov3,4
1Siberian Federal University, Krasnoyarsk, 660041, Russia
2Krasnoyarsk State Agrarian University, Krasnoyarsk, 660049, Russia
3Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
4Novosibirsk State University, Novosibirsk, 630090, Russia
Keywords: численные методы, константы диссипации, импульсное нагружение, упругие деформируемые тела, numerical methods, dissipation constants, pulsed loading, elastic deformable solids

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.