Zur klassischen Kontaktaufgabe der Elastostatik

Abstract

For the study of boundary contact problems of thermoelastostatics, thermoelastic vibrations and other models with boundary integral methods the main difficulty which arises is, that displacement and stress contact conditions are to fulfil on the contact-surface between the elastic homogeneous parts. To solve these difficulties one is forced to study the contact problem of elastostatics. It is proved that an earlier potential representation is proper for getting some better results: 1. The boundary integral operator $\mathcal{K}$ of the contact problem is invertible without any assumption on the Poisson rations of the elastic parts. 2. $\mathcal{K}$ is a strongly elliptic pseudodifferential operator of order zero. Therefore theorems on asymptotic error estimates for boundary element methods are applicable.