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On three-dimensional effects near the vertex of a crack in a thin plate. (English. Russian original) Zbl 0787.73059

J. Appl. Math. Mech. 55, No. 3, 407-415 (1991); translation from Prikl. Mat. Mekh. 55, No. 3, 500-510 (1991).
Summary: The influence of the face profile of a crack on the stress-strain state of a thin plate is discussed. A three-dimensional boundary layer appears in the immediate neighbourhood of the crack ends, while linear combinations of special singular solutions of the generalized plane- stress state serve as asymptotic correction terms far from the ends of the crack. The energy-balance formula for crack propagation is sharpened. Formulations of two-dimensional problems which include two asymptotic terms are indicated, (and, in particular, the idea of an effective plane- projected crack length is introduced).

MSC:

74R99 Fracture and damage
74K20 Plates
35Q72 Other PDE from mechanics (MSC2000)
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