Сибирский федеральный университет

Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций

Конференция: International Conference on Numerical Analysis and Applications, NAA 2012; Lozenetz; Lozenetz

Год издания: 2013

Идентификатор DOI: 10.1007/978-3-642-41515-9_54

Ключевые слова: computational algorithm, discontinuous solution, dynamics, elasticity, granular medium, plastic shock wave, variational inequality

Аннотация: Mathematical models of the dynamics of elastic-plastic and granular media are formulated as variational inequalities for hyperbolic operators with one-sided constraints describing the transition of a material in plastic state. On this basis a priori integral estimates are constructed in characteristic cones of operators, from which follows the uniqueness and continuous dependence on initial data of solutions of the Cauchy problem and of the boundary-value problems with dissipative boundary conditions. With the help of an integral generalization of variational inequalities the relationships of strong discontinuity in dynamic models of elastic-plastic and granular media are obtained, whose analysis allows us to calculate velocities of shock waves and to construct discontinuous solutions. Original algorithms of solution correction are developed which can be considered as a realization of the splitting method with respect to physical processes. © 2013 Springer-Verlag.

Журнал: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Выпуск журнала: Vol. 8236 LNCS

Номера страниц: 479-486

ISSN журнала: 03029743

• Sadovskii V.M. (Institute of Computational Modeling SB RAS, Akademgorodok 50/44, 660036 Krasnoyarsk, Russian Federation)

• Scopus