| Autor: |
Imai, Ryuta, Yamada, Masayuki, Hada, Koji, Fujiwara, Hiroyuki |
| Zdroj: |
GEM: International Journal on Geomathematics; 2025, Vol. 16 Issue 1, p1-29, 29p |
| Abstrakt: |
We derive a general form of the complex stress function for the plane strain problem, which represents the stress field around kinked or branched faults. Specifically, the general solution is established as the sum of a particular solution and a homogeneous solution. The particular solution is constructed by pulling back the known complex stress function around a flat fault into the computational space using the Joukowski transformation and pushing it forward into the physical space around a kinked fault using the Schwarz–Christoffel transformation. Additionally, the homogeneous solution is shown to be a Laurent series with positive terms up to the first order at most. Detailed discussions on inequality estimates and the asymptotic behavior for the Schwarz–Christoffel transformation and the Kolosov–Muskhelishvili's formlua are provided. It is shown that the representation formula provides accurate results even for kinked faults, which are difficult to compute numerically by the finite element method. Furthermore, as an application of the representation formula for the complex stress function around a kinked fault, the stress singularity of the kinking point is evaluated. In particular, the stress singularity is found to depend monotonically and increasingly on the external angle of the kinking point. Consequently, stress singularity exists on the front side of the kinking point but not on the back side, except under unphysical conditions. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
|
Full text from SpringerLink