The Problem of Collective Identation of an Elastic Half-Plane by a System of Rigid Punches Elastically Connected to a Common Platform

The problem is considered for the indentation of an elastic half-plane by a system of rigid punches elastically connected to a common rigid platform. A variational formulation of the problem are obtained in the form of a boundary variational inequality using the Poincare-Steklov operator for an elastic half-plane. A minimization problem equivalent to the variational inequality is given, for approximation of which the boundary-element approach is used. As a result, a quadratic programming problem with equality and inequality restrictions is obtained, for the numerical solution of which an algorithm based on the conjugate gradient method was used. Patterns of collective indentation of elastic half-plane by a system of rigid punches elastically connected to a common platform have been investigated by computational experiment.