A potential problem arising from the strip-punch problem in elasticity (Q1113735)

Three-dimensional contact problems in the classical theory of linear elasticity can often be regarded as mixed boundary-value problems of potential theory. In this paper we examine the problem where contact between the indenting object (called a punch) and the elastic medium is maintained over an infinite strip. It is assumed that a rigid frictionless punch with a known profile has intended a homogeneous, isotropic and linearly elastic half-space. Applying the theory of Mathieu functions, an analytic solution of Laplace's equation is obtained through separation of variables in the elliptic cylinder coordinate system. Finally three examples are discussed where in each case the normal component of stress under the punch is numerically evaluated.