Non-unique solution with discontinuous velocity for collision of elastic bar with high initial speed by ST-PDAS restoring energy

Non-unique solution with discontinuous velocity for collision of elastic bar with high initial speed by ST-PDAS restoring energy Научная публикация

Журнал

Journal of Mathematical Sciences (United States)
ISSN: 1072-3374

Вых. Данные

Год: 2026, Страницы: 1-16 Страниц : 16 DOI: 10.1007/s10958-026-08266-w

Ключевые слова

Impact contact dynamics , Variational inequality, Discontinuous velocity, Space-time finite element , Primal-dual active set

Авторы

Victor A. Kovtunenko ^1,2

Организации

1	Department of Mathematics and Scientific Computing, University of Graz, NAWI Graz, Heinrichstr.36, Graz, 8010, Austria
2	Lavrent’ev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, Novosibirsk, 630090, Russia

Motivated by inequality constraints appearing in optimization context, we study non-smooth variational problems and methods appropriate for their accurate solution. The use of Lagrange multipliers and merit functions leads to semi-smooth Newton methods and equivalent primal-dual active-set iterative algorithms. For application in dynamic contact mechanics, we investigate the collision of a rigid obstacle by a one-dimensional elastic bar. The problem is described by the wave equation subjected to complementarity conditions, which weak solution is characterized by a discontinuous velocity. The collision problem may have a non-unique solution for a high initial speed exceeding the propagation speed of elastic waves. Multiple solutions are constructed analytically. For the unique solution that restores the energy of the bar after rebound, the primal-dual active-set method is implemented within space-time finite elements.

Victor A. Kovtunenko
Non-unique solution with discontinuous velocity for collision of elastic bar with high initial speed by ST-PDAS restoring energy
Journal of Mathematical Sciences (United States). 2026. P.1-16. DOI: 10.1007/s10958-026-08266-w Scopus OpenAlex

Поступила в редакцию:	1 дек. 2025 г.
Принята к публикации:	25 февр. 2026 г.
Опубликована online:	6 мар. 2026 г.

≡ Scopus:	2-s2.0-105033789206
≡ OpenAlex:	W7134037090