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

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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.

Abstract

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.

참고문헌 (14)

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  7. R. V. Namm, "A modied dual scheme for solving an elastic crack problem, Numer. Anal. Appl. 10 (2017), no. 1, 37-46", Sib. Zh. Vychisl. Mat, 20(1), pp.47~58 (2017), Publishing House SB RAS[DOI]
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  9. E. M. Rudoy, "Numerical solution of an equilibrium problem for an elastic body with a thin delaminated rigid inclusion, J. Appl. Ind. Math. 10 (2016), no. 2, 264-276", Sib. Zh. Ind. Mat, 19(2), pp.74~87 (2016)[DOI]
  10. F. P. Vasiliev, "Methods for Solving Extremal Problems" (1981), Nauka
  11. E. M. Vikhtenko, "A duality scheme for solving the semi-coercive Signorini problem with friction, Comput. Math. Math. Phys. 47 (2007), no. 12, 1938-1951", Zh. Vychisl. Mat. Mat. Fiz, 47(12), pp.2023~2036 (2007), Pleiades Publishing Ltd[DOI]
  12. E. M. Vikhtenko, "Sensitivity functionals in contact problems of elasticity theory", Computational Mathematics and Mathematical Physics, 54(7), pp.1190~1200 (2014), Pleiades Publishing Ltd[DOI]
  13. E. M. Vikhtenko, "The methods for solving semicoercive variational inequalities of mechanics on the basis of modied Lagrangian functionals", Dal'nevost. Mat. Zh, 14(1), pp.6~17 (2014)
  14. E. M. Vikhtenko, "A modied duality scheme for nite-and innite-dimensional convex program-ming problems", Dal'nevost. Mat. Zh, 17(2), pp.158~169 (2017)

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