Numerical analysis for a new kind of obstacle problem

Analysis of an elastic–rigid obstacle problem described by a variational–hemivariational inequality

“…\end{eqnarray}$$Problem P is the same as the model studied in Cheng et al. [2]. Thus, the model considered here is more general.…”

“…Under the circumstances, the weak form of the obstacle model is a variational–hemivariational inequality, instead of a variational inequality considered in Cheng et al. [2].…”

“…The obstacle problem consists in finding the equilibrium position of an elastic membrane, which (i) passes through the boundary of a bounded domain Ω; (ii) is subject to the action of a vertical force 𝑓 ∈ 𝐿 2 (Ω); (iii) lies above an obstacle [9]. Since the region of contact between the obstacle and the membrane is not known a priori, the problem is nonlinear.…”

“…However, the obstacle is not always perfectly rigid in practice. A new kind of obstacle model is proposed in Cheng et al [2], in which the obstacle is made of a rigid body covered by a soft layer. The layer is deformable and allows a linear reactive normal force with respect to the interpenetration between the membrane and the obstacle.…”

“…In this paper, we consider a more general case, in which the reactive normal force may be nonmonotone with respect to the penetration. Under the circumstances, the weak form of the obstacle model is a variational-hemivariational inequality, instead of a variational inequality considered in Cheng et al [2].…”