Numerical investigation of the 2d–1d structure interaction model

Abstract

In this article, we explore the possibility of modeling the interaction of a 2d elastic body with a thin 2d elastic body of possibly higher thickness using a 1d model for the thin body. We use the asymptotic analysis with respect to the small thickness of the 2d interaction model and formulate five different limit models depending on the order of stiffness of the thin body with respect to the thickness. Then we formulate a 2d–1d model which has the same asymptotics as the 2d–thin 2d model with respect to thickness. Finally, we numerically test the approximation of the 2d–thin 2d model by the 2d–1d model on two problems, one with an analytical solution and one more realistic problem.