A COMPLEX VARIABLE SOLUTION FOR A DEFORMING CIRCULAR TUNNEL IN AN ELASTIC HALF-PLANE

✍ Scribed by Verruijt, A.

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 308 KB
• Volume: 21
• Category: Article
• ISSN: 0363-9061
• DOI: 10.1002/(sici)1096-9853(199702)21:2<77::aid-nag857>3.0.co;2-m

✦ Synopsis

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.