Contact with a Corner for Nonlinearly Elastic Rods
In elastic contact problems it is usually required that the contact force has to be directed normally to the contact surface in the absence of friction. For an obstacle with nonsmooth surface this gives infinitely many normal directions at an edge or at a corner. For the case where a nonlinearly elastic rod under terminal loads is hanging over a needle, it is shown that the balance equations supplemented with such a normality condition have a continuum of solutions. Moreover, an additional contact condition is derived from a corresponding variational problem by means of special inner variations that preserve the shape of the rod. This way one is finally lead to a unique solution at least locally.
KeywordsElastic rods Contact problems Nonlinear elasticity Variational methods
Mathematics Subject Classification34A34 49J52 74B20 74K10
- 2.Konz, V.: Ein spezielles Kontaktproblem für nichtlinear elastische Stäbe. Diploma thesis, Universität zu Köln (2006) Google Scholar