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Nonlinear Flamant problem

David J. Unger
Vol. 20 (2025), No. 3, 353–362
DOI: 10.2140/jomms.2025.20.353
Abstract

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.

Keywords
point load, residual stress, Duffing equation, shot peening \unskip
Milestones
Received: 22 April 2025
Revised: 25 July 2025
Accepted: 1 August 2025
Published: 2 September 2025
Authors
David J. Unger
Mechanical and Civil Engineering
University of Evansville
Evansville, IN 47722
United States
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