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Analytical solution of a variational inequality for a cutted bar. (English) Zbl 0863.73077
The equilibrium problem of a clamped elastic bar with a vertical crack is considered. A nonpenetration condition of the crack banks leads to the restriction imposed upon the solution as an inequality. This model is described by the elliptic variational inequality. We construct the analytical solution of the problem using the projection of the initial space onto the set of solutions with the restriction.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74R99 Fracture and damage
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