caa a22 4500 469124334 CHVBK 20180323133147.0 cr unu---uuuuu 170328e19920601xx s 000 0 eng 10.1007/BF00032513 doi (NATIONALLICENCE)springer-10.1007/BF00032513 Some reverse mappings in 3-D crack and dislocation problems [Elektronische Daten] [Z. Yong, M. Hanson] A new division of geometric regions for internal and external planar cracks is introduced. This allows some reverse mappings between internal and external problems to be revealed in connection with 3-D planar crack and dislocation problems in an infinite elastic medium. Transform factors are given for a mode I crack with arbitrary shape in an infinite inhomogeneous isotropic medium where the elastic modulus is an exponential function of depth. Arbitrary loading for the inhomogeneous material and coplanar dislocation-crack interaction for a homogeneous isotropic medium are analyzed through easy derivations. As one of the applications, the known solution of an external elliptical crack is used to obtain the exact solution in closed form for the crack with the boundary contour % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyWdiNaai% ikaiabeI7aXjaacMcacqGH9aqpcaWGIbWaaWbaaSqabeaacaaIYaaa% aOWaaOaaaeaadaWcaaqaaiGacogacaGGVbGaai4CamaaCaaaleqaba% GaaGOmaaaakiabeI7aXbqaaiaadggadaahaaWcbeqaaiaaikdaaaaa% aOGaey4kaSYaaSaaaeaaciGGZbGaaiyAaiaac6gadaahaaWcbeqaai% aaikdacqaH4oqCaaaakeaacaWGIbWaaWbaaSqabeaacaaIYaaaaaaa% aeqaaaaa!4F66!\[\rho (\theta ) = b^2 \sqrt {\frac{{\cos ^2 \theta }}{{a^2 }} + \frac{{\sin ^{2\theta } }}{{b^2 }}} \]subjected to a pair of concentrated forces at the crack center. Kluwer Academic Publishers, 1992 Yong Z. Department of Engineering Mechanics, University of Kentucky, 40506-0046, Lexington, Kentucky, USA aut Hanson M. Department of Engineering Mechanics, University of Kentucky, 40506-0046, Lexington, Kentucky, USA aut International Journal of Fracture Kluwer Academic Publishers 55/3(1992-06-01), 245-259 0376-9429 55:3<245 1992 55 10704 https://doi.org/10.1007/BF00032513 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00032513 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yong Z. Department of Engineering Mechanics, University of Kentucky, 40506-0046, Lexington, Kentucky, USA aut NATIONALLICENCE 700 1- Hanson M. Department of Engineering Mechanics, University of Kentucky, 40506-0046, Lexington, Kentucky, USA aut NATIONALLICENCE 773 0- International Journal of Fracture Kluwer Academic Publishers 55/3(1992-06-01), 245-259 0376-9429 55:3<245 1992 55 10704 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer