A plane stress nonlinear point load problem is addressed analytically on a half-plane
by using a technique based on a one-parameter group transformation that admits a
similarity solution. An exact solution for the stress field is expressed in terms of a
Jacobian elliptic function. As this stress acts only in the radial direction from
the point of application, it parallels the solution found for the linear elastic
Flamant problem. The corresponding strain field is composed of both elastic
and inelastic components, which collectively satisfy a derived compatibility
equation. A possible application for the solution involving residual stress is
discussed.
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