Geodesic
A choice of an optimal form of surface cracks in 3D solids
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 2, pp. 76-87

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We consider 3D-elastic body with a surface crack satisfying a nonpenetration conditions (Signorini-type conditions). In the paper, we investigate two optimization problems. The first problem is to find the crack shape which gives the minimum deviation of the energy functional derivative from a given critical value. The second one is to investigate a solvability of an optimization problem of a crack path with a cost functional depending on the derivative of the energy functional and a crack surface area. 
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     author = {E. M. Rudoy},
     title = {A choice of an optimal form of surface cracks in {3D} solids},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {76--87},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2006_6_2_a5/}
}
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E. M. Rudoy. A choice of an optimal form of surface cracks in 3D solids. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 2, pp. 76-87. http://geodesic.mathdoc.fr/item/VNGU_2006_6_2_a5/