This article is cited in 15 papers

The method of smooth domains in the equilibrium problem for a plate with a crack

A. M. Khludnev

M. A. Lavrent'ev Institute of Hydrodynamics

Abstract: A free boundary problem is considered of the equilibrium of an elastic plate with a crack. We suppose that some boundary mutual nonpenetration conditions are given on the crack faces in the form of simultaneous equalities and inequalities. We suggest a new approach to posing the problem in a smooth domain although it was stated in a domain with cuts originally. We treat the constraints on the components of the displacement vector and stress tensor on the crack faces as interior constraints, i.e. constraints given on subsets of the smooth domain of a solution.

Keywords: plate, nonsmooth domain, boundary value problem, crack.

UDC: 517.958

Received: 08.02.2002

 English version: Siberian Mathematical Journal, 2002, 43:6, 1124–1134

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