Premium
A COMPLEX VARIABLE SOLUTION FOR A DEFORMING CIRCULAR TUNNEL IN AN ELASTIC HALF‐PLANE
Author(s) -
Verruijt A.
Publication year - 1997
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/(sici)1096-9853(199702)21:2<77::aid-nag857>3.0.co;2-m
Subject(s) - conformal map , displacement (psychology) , laurent series , geometry , constant (computer programming) , mathematics , plane (geometry) , series (stratigraphy) , deformation (meteorology) , computation , boundary (topology) , mathematical analysis , boundary value problem , stress (linguistics) , mechanics , physics , geology , psychology , paleontology , linguistics , philosophy , algorithm , meteorology , computer science , psychotherapist , programming language
An analytical solution is presented of problems for an elastic half‐plane with a circular tunnel, which undergoes a certain given deformation. The solution uses complex variables, with a conformal mapping onto a circular ring. The coefficients in the Laurent series expansion of the stress functions are determined by a combination of analytical and numerical computations. As an example the case of a uniform radial displacement of the tunnel boundary is considered in some detail. It appears that a uniform radial displacement is accompanied by a downward displacement of the tunnel as a whole. This phenomenon also means that the distribution of the apparent spring constant is strongly non‐uniform. © 1997 by John Wiley & Sons, Ltd.