An Optimal Size of a Rigid Thin Stiffener Reinforcing an Elastic Two-Dimensional Body on the Outer Edge

Nyurgun Lazarev () and Galina Semenova ()
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Nyurgun Lazarev: North-Eastern Federal University
Galina Semenova: North-Eastern Federal University

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 2, No 14, 614-626

Abstract: Abstract The equilibrium problem for a two-dimensional body with a crack is studied. We suppose that the body consists of two parts: an elastic part and a rigid thin stiffener on the outer edge of the body. Inequality-type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. For a family of variational problems, dependence of their solutions on the length of the thin rigid stiffener is investigated. It is shown that there exists a solution of an optimal control problem. For this problem, the cost functional is defined by a continuous functional on a solution space, while the length parameter serves as a control parameter.

Keywords: Variational inequality; Optimal control problem; Non-penetration condition; Crack; Energy functional; 49J40; 49J20; 74G55; 74R10 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-018-1291-8

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