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The dynamics of an elliptical crack in an elastic space: Solution using Padé approximations. (English. Russian original) Zbl 0789.73055

J. Appl. Math. Mech. 55, No. 3, 416-423 (1991); translation from Prikl. Mat. Mekh. 55, No. 3, 511-519 (1991).
Dynamic problems in the theory of elasticity involving normal cleavage cracks in an unbounded linearly-elastic space under harmonically varying and impact loads are considered. The study involves a reduction of the problem to integrodifferential equations for normal jump displacements on the crack surface. The method used to solve these is based on Padé approximations (PA). The use of this method requires a very accurate representation of the coefficients of a Taylor series expansion of the solution. Thus, the problem of the harmonic effects is solved using PA only for elliptical cracks, when the coefficients of the Taylor series expansion with respect to the wave number are expressed in analytical form.

MSC:

74R99 Fracture and damage
41A21 Padé approximation
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References:

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