Derivatives of the energy functional for 2D-problems with a crack under Signorini and friction conditions. (English) Zbl 0954.35076

Bach, Michael; Khludnev, Alexander M.; Kovtunenko, Victor A.

Math. Methods Appl. Sci. 23, No. 6, 515-534 (2000).

The two-dimensional elasticity problem for an elastic body with a crack is investigated. In the result of the study of the derivatives of the energy functional with respect to the crack length the criterion for the crack growing is established. The representation for the singular solution of the Lamé system is received. The derivative of the potential energy for the obtained singular solution is calculated.

Reviewer: R.M.Dzhafarov (Donetsk)

MSC:

35J85	Unilateral problems; variational inequalities (elliptic type) (MSC2000)
49Q12	Sensitivity analysis for optimization problems on manifolds
74R99	Fracture and damage

Keywords:

solid; crack; singularity; variational inequality; variation of shape

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