Abstract
A nonlinear eigenvalue problem related to determining the stress and strain fields near the tip of a transverse crack in a power-law material is studied. The eigenvalues are found by a perturbation method based on representations of an eigenvalue, the corresponding eigenfunction, and the material nonlinearity parameter in the form of series expansions in powers of a small parameter equal to the difference between the eigenvalues in the linear and nonlinear problems. The resulting eigenvalues are compared with the accurate numerical solution of the nonlinear eigenvalue problem.
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Original Russian Text © L.V. Stepanova, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 8, pp. 1399–1415.
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Stepanova, L.V. Eigenvalue analysis for a crack in a power-law material. Comput. Math. and Math. Phys. 49, 1332–1347 (2009). https://doi.org/10.1134/S0965542509080053
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DOI: https://doi.org/10.1134/S0965542509080053