A Modified Duality Method for Solving an Elasticity Problem with a Crack Extending to the Outer Boundary
A modified dual method for solving an elasticity problem with a crack extending to the outer boundary is considered. The method is based on a modified Lagrange functional. The convergence of the method is investigated in detail under a natural assumption of \(H^1\)-regularity of the solution to the crack problem. Basic duality relation for the primal and dual problems is proposed.
KeywordsNon-penetration condition Crack Duality scheme Modified lagrange functional Generalized newton method
This study was supported by the Russian Foundation for Basic Research (Project 17-01-00682 A). Numerical experiments were performed on a computational cluster of the Shared Facility Center “Data Center of FEB RAS” .
- 1.Morozov, N.F.: Mathematical Problems of Crack Theory. Nauka, Moscow (1982)Google Scholar
- 2.Khludnev, A.M.: Problems of Elasticity Theory in Non-Smooth Domains. Fizmatlit, Moscow (2010)Google Scholar
- 3.Kravchuk, A.S.: Variational and Quasi-Variational Inequalities in Mechanics. MGAPI, Moscow (1997)Google Scholar
- 14.Hlavačhek, I., Haslinger, Ya., Nechas, I., Lovišhek, Ya.: Numerical Solution of Variational Inequalities. Springer, New York (1988)Google Scholar
- 15.Kufner, A., Fuchik, S.: Nonlinear Differential Equations. Nauka, Moscokw (1988)Google Scholar
- 16.Vasiliev, F.P.: Methods for Solving Extremal Problems. Nauka, Moscow (1981)Google Scholar
- 20.Shared Facility Center “Data Center of FEB RAS” (Khabarovsk). http://lits.ccfebras.ru