Numerical solution of dynamic problems of elastoplastic deformation of solids

I. O. Bogulskii^a, Yu. M. Volchkov<sup>bc

a</sup> Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk
^b M. A. Lavrent'ev Institute of Hydrodynamics, Novosibirsk
^c Novosibirsk State University, Novosibirsk

Abstract: Numerical algorithms for solving two-dimensional dynamic problems of elasticity theory were developed based upon several local approximations for each of the required functions. The schemes contain free parameters (constants of dissipation). The explicit form for formulas of the artificial dissipation of solutions allows us to control its size and to build effective both explicit and implicit schemes. As an example, the principle of constructing such schemes is presented for a plane dynamic problem of elasticity theory. We describe a class of problems, for which numerical algorithms are constructed using several local approximations for each of the required functions. Examples of solving applied problems are given.

Key words: dynamic problem of elasticity theory, local approximation of required functions, implicit and explicit finite difference schemes.

UDC: 539.3+519.6

Received: 31.10.2011

 English version: Numerical Analysis and Applications, 2012, 5:2, 124–128

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