Abstract
The axisymmetric meridional flow of an incompressible perfectly rigid-plastic medium between two concentric rough spheres, such that the outer sphere is fixed and the surface of the inner one is uniformly expanded, is studied in the case of a sink. Two problem statements are considered: quasistatic and dynamic. An asymptotic integration of a boundary value problem with a natural small geometric parameter equal to the ratio of the distance between concentric spheres to the inner radius is performed. The dynamic statement of the problem includes one more dimensionless parameter which does not depend on time (in contrast to geometric one) and equals to the inverse Euler number. This value is also taken much less than one. Depending on the ratio of these parameters, i.e., at different time intervals, using the asymptotic integration procedure, the coefficients of several principal terms in the expansions for both velocities and stresses are obtained in analytical form.
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Georgievskii, D., Shabaykin, R. (2021). Quasistatic and Dynamic Deformation of an Asymptotically Thin Perfectly Rigid-Plastic Spherical Layer. In: Altenbach, H., Eremeyev, V.A., Igumnov, L.A. (eds) Multiscale Solid Mechanics. Advanced Structured Materials, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-030-54928-2_12
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