On modeling elastic bodies with defects
type: Item
instance of: scholarly article
title: On modeling elastic bodies with defects
zbMATH Open document ID: 1390.35354
author: Alexander Khludnev
publication date: 2018-04-03T00:00:00Z
review text: In this paper, the author considers some mathematical analysis problems on the equilibrium for 2D elastic bodies with thin defects, which are characterized with a damage parameter. Solution existence of the problems considered is proved, and different equivalent problem formulations are proposed. Dependence of solutions on the damage parameter and the defect length is investigated. The author derives a formula for the derivative of the energy functional with respect to the defect length and prove that the formula can be written in the form of an invariant integral. An optimal control problem is investigated with a cost functional equal to the derivative of the energy functional with respect to the defect length, and the damage parameter being a control function.
reviewed by: Dongbing Zha
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 35Q93
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 74R05
Mathematics Subject Classification ID: 93C23
zbMATH DE Number: 6855321
zbMATH Keywords: defect
zbMATH Keywords: damage parameter
zbMATH Keywords: non-penetration boundary conditions
zbMATH Keywords: variational inequality
zbMATH Keywords: optimal control
zbMATH Keywords: derivative of energy functional
MaRDI profile type: Publication
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DOI: 10.17377/SEMI.2018.15.015
published in: Sibirskie Elektronnye Matematicheskie Izvestiya
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description: scientific article; zbMATH DE number 6855321