Communications of the
Korean Mathematical Society CKMS

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Commun. Korean Math. Soc. 2019; 34(4): 1353-1364

Online first article August 27, 2019      Printed October 31, 2019

https://doi.org/10.4134/CKMS.c180350

Copyright © The Korean Mathematical Society.

Modified Lagrange functional for solving elastic problem with a crack in continuum mechanics

Robert V. Namm, Georgiy I. Tsoy, Gyungsoo Woo

Computing Center of Far Eastern Branch Russian Academy of Sciences; Computing Center of Far Eastern Branch Russian Academy of Sciences; Changwon National University

Abstract

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Modified Lagrange functional for solving an elastic problem with a crack is considered. Two formulations of a crack problem are investigated. The first formulation concerns a problem where a crack extending to the outer boundary of the domain. In the second formulation, we consider a problem with an internal crack. Duality ratio is established for initial and dual problem in both cases.

Keywords: elasticity, duality scheme, crack problem, modified Lagrange functional

MSC numbers: 65F10, 65K10, 49M15, 74G15, 74G65

Supported by: The first two authors were supported by the Russian Foundation for Basic Research (Project 17-01-00682 A).

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