A three-dimensional parabolic punch problem in linear elasticity. (English) Zbl 0725.73078
Summary: In this paper an analytic solution for a three-dimensional contact problem, in linear elasticity, is constructed through the separation of Laplace’s equation in paraboloidal coordinates. A rigid punch under normal loading is applied to an isotropic elastic medium occupying an infinite half-space where the contact region is parabolic and the punch profile is prescribed. This treatment allows for a general punch profile provided it is physically reasonable so as to ensure the convergence of the solution.
MSC:
| 74A55 | Theories of friction (tribology) |
| 74M15 | Contact in solid mechanics |
| 74B99 | Elastic materials |
| 74H99 | Dynamical problems in solid mechanics |
Keywords:
Mathieu functions; separation of Laplace’s equation; paraboloidal coordinates; rigid punch; normal loading; isotropic elastic medium; infinite half-spaceSoftware:
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