This article is cited in 3 papers

Differentical equations, dynamical systems and optimal control

Equilibrium problem for an thermoelastic Kirchhoff–Love plate with a nonpenetration condition for known configurations of crack edges

N. P. Lazarev

North-Eastern Federal University, 48, Kulakovsky str., Yakutsk, 677000, Russia

Abstract: We formulate a new variational problem on the equilibrium of a thermoelastic Kirchhoff–Love plate in a domain with a cut. It is assumed that the plate is under the special loads for which the configuration of crack's edges is known in advance. This circumstance makes it possible to write down the general boundary condition of nonpenetration in a refined form, which, in turn, leads to new relations describing the possible mechanical interaction of opposite crack edges. The initial formulation of a problem presupposes the fulfillment of boundary conditions on the crack curve in the form of system of two inequalities and an equality. Solvability of the problem is proved, an equivalent differential setting is found.

Keywords: thermoelastic plate, crack, non-penetration, variational inequality, differential setting.

UDC: 517.9

MSC: 49J40

Received November 11, 2020, published December 21, 2020

Language: English

DOI: 10.33048/semi.2020.17.140

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