التفاصيل البيبلوغرافية
| العنوان: |
Annular and circular rigid inclusions planted into a penny-shaped crack and factorization of triangular matrices. |
| المؤلفون: |
Antipov, Y. A., Mkhitaryan, S. M. |
| المصدر: |
Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences; Jun2020, Vol. 476 Issue 2238, p1-20, 20p |
| مصطلحات موضوعية: |
MATRIX decomposition, RIEMANN-Hilbert problems, INTEGRAL equations, EXPONENTIAL functions, ANALYTICAL solutions, MATHEMATICAL convolutions |
| مستخلص: |
Analytical solutions to two axisymmetric problems of a penny-shaped crack when an annulus-shaped (model 1) or a disc-shaped (model 2) rigid inclusion of arbitrary profile are embedded into the crack are derived. The problems are governed by integral equations with the Weber-Sonine kernel on two segments. By the Mellin convolution theorem, the integral equations associated with models 1 and 2 reduce to vector Riemann-Hilbert problems with 3 ×3 and 2× 2 triangular matrix coefficients whose entries consist of meromorphic and plus or minus infinite indices exponential functions. Canonical matrices of factorization are derived and the partial indices are computed. Exact representation formulae for the normal stress, the stress intensity factors (SIFs) at the crack and inclusion edges, and the normal displacement are obtained and the results of numerical tests are reported. In addition, simple asymptotic formulae for the SIFs are derived. [ABSTRACT FROM AUTHOR] |
|
Copyright of Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences is the property of Royal Society and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
| قاعدة البيانات: |
Complementary Index |
