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Application of Padé approximation for solving dynamical problems of elasticity for a space weakened by a plane crack. (Russian) Zbl 0717.73089
The dynamical problem of elasticity for a crack in an infinite linear elastic space under harmonically varying action is considered. The authors present a constructive procedure for expanding the solution into an infinite series in powers of the wave number \(\beta\). Since this series converges only for sufficiently small \(\beta\), the continuation of solution by using Padé approximation is proposed. The obtained results are compared with known ones; the accuracy and efficiency of a numerical method used for solving the problem are discussed.
Reviewer: O.Titow

74S30 Other numerical methods in solid mechanics (MSC2010)
74R99 Fracture and damage
41A21 Padé approximation