Flat punch of arbitrary shape on an elastic half-space
A new method is proposed for the analysis of elastic contact problems for a flat punch of arbitrary planform under the action of a normal centrally applied force. The method is based of an integral representation for the reciprocal distance between two points obtained by the author earlier [Izv. Vyssh. Uchebn. Zaved., Mat. 1971, No.2(105), 102-104 (1971; Zbl 0221.45006)]. A simple yet accurate relationship is established between the punch settlement and the applied force for an arbitrary flat punch. Specific formulae are derived for a punch whose planform has a shape of a polygon, a triangle, a rectangle, a rhombus, a circular sector and a circular segment. All the formulae are checked against the solutions known in the literature, and a good accuracy is confirmed.
scientific article; zbMATH DE number 3970271