Geodesic
Ray approximations for the shock waves of an elastic deformation of axisymmetric type in a~cylindrical layer
Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 2, pp. 111-123

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The efficiency of the version of the ray method developed directly for strong discontinuity waves (shock waves) is demonstrated by the example of an axisymmetric problem of intense deformation of a cylindrical nonlinear elastic layer under load action on its exterior border. We consider several initial stages of the wave process, namely, the motion of the created shock waves to the interior border of the layer, the reflection of a more rapid wave from the interior border, the interaction of a slow shock wave and the reflected shock wave with the formation of a new wave pattern. The solution for each deformation stage is constructed using the modified ray series method.
Keywords: nonlinear elastic medium, impact deformation, ray series, axisymmetric problem, quasi-longitudinal and quasi-transverse shock waves. 
@article{SJIM_2015_18_2_a10,
     author = {V. E. Ragozina and Yu. E. Ivanova},
     title = {Ray approximations for the shock waves of an elastic deformation of axisymmetric type in a~cylindrical layer},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {111--123},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2015_18_2_a10/}
}
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V. E. Ragozina; Yu. E. Ivanova. Ray approximations for the shock waves of an elastic deformation of axisymmetric type in a~cylindrical layer. Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 2, pp. 111-123. http://geodesic.mathdoc.fr/item/SJIM_2015_18_2_a10/