The indentation problem of rigid punch with curvilinear base on elastic half-space is solved by variational method. The method is based on Betti theorem and on condition of absence of stress singularity at the edge of contact spot. Variation condition of absence of stress singularity at the edge of contact spot gives the equations connecting the displacement and the size and the shape of the contact spot and gives the expression for contact stress under curvilinear base of punch. The case of elliptical contact spot is considered.
Variational Approach in Elastic-Indentation Problems
Riznychuk, RV. "Variational Approach in Elastic-Indentation Problems." Proceedings of the World Tribology Congress III. World Tribology Congress III, Volume 1. Washington, D.C., USA. September 12–16, 2005. pp. 391-392. ASME. https://doi.org/10.1115/WTC2005-64014
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