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Application of the finite element iterative method to the eigenvalue problem of a crack between dissimilar media
Author(s) -
Barsoum Roshdy S.
Publication year - 1988
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620260303
Subject(s) - eigenvalues and eigenvectors , finite element method , eigenfunction , singularity , stress intensity factor , iterative method , matrix (chemical analysis) , mathematics , mathematical analysis , stress (linguistics) , structural engineering , materials science , mathematical optimization , physics , engineering , composite material , quantum mechanics , linguistics , philosophy
The finite element iterative method is applied to the eigenvalue problem of a crack between dissimilar media. In this case the transfer matrix is non‐symmetric, which leads to complex eigenvalues. The singularity obtained agrees with the analytical results of r (−1/2+ ie ) . The method of evaluating the eigenfunctions is general and can be applied to more complex cases of material and geometry, which are frequently encountered in composite materials. A powerful method for evaluating stress intensities in dissimilar media is given in the Appendix. The method is also reduced for homogeneous media to give stress intensity factors for modes I, II and III.