Modelling, Analysis and Numerical Simulation of a Spring-Rods System with Unilateral Constraints

Autor:	Ochal, Anna, Prządka, Wiktor, Sofonea, Mircea, Tarzia, Domingo A.
Rok vydání:	2023
Předmět:	Mathematics - Numerical Analysis Mathematical Physics Mathematics - Classical Analysis and ODEs 74K10 74K05 74M15 74G35 74G30 74G15 49J40
Druh dokumentu:	Working Paper
Popis:	In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the problem, then we state and prove some convergence results, for which we provide the corresponding mechanical interpretation. Next, we turn to the numerical approximation of the problem based on a finite element scheme. We use a relaxation method to solve the discrete problems that we implement on the computer. Using this method, we provide numerical simulations which validate our convergence results. Comment: 24 pages, 8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.04365 Zobrazit plný text záznamu View this record from Arxiv