Modelling, analysis, and numerical simulation of a spring-rods system with unilateral constraints

OCHAL, ANNA; PRZ?DKA, WIKTOR; SOFONEA, MIRCEA; TARZIA, DOMINGO A

MATHEMATICS AND MECHANICS OF SOLIDE

SAGE Publications Inc.

Año: 2024 vol. 29 p. 246 - 263

1081-2865

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.