Analysis of the structure of the boundary layer in the problem of the torsion of a laminated spherical shell |
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| Authors: | NK Akhmedov Yu A Ustinov |
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| Institution: | 1. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland;2. Warsaw University of Technology, Department of Vehicles, 84 Narbutt Str., 02-524 Warsaw, Poland;3. Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, Politekhnicheskaya 77, 410054 Saratov, Russian Federation;4. Department of Mathematics and Modeling, Saratov State Technical University, Politekhnicheskaya 77, 410054 Saratov, Russian Federation;1. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland;2. Department of Vehicles, Warsaw University of Technology, 84 Narbutta Str., 02-524 Warsaw, Poland;3. Cybernetic Institute, National Research Tomsk Polytechnic University, 30 Lenin Avenue, 634050 Tomsk, Russian Federation;4. Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, 77 Politehnicheskaya Str., 410054 Saratov, Russian Federation;5. Department of Mathematics and Modeling, Saratov State Technical University, 77 Politehnicheskaya Str., 410054 Saratov, Russian Federation |
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| Abstract: | The structures of the boundary layer in the problem of the torsion of a radially stratified spherical segment (shell) with an arbitrary number of alternating hard and soft layers are investigated. It is shown that weakly attenuating boundary-layer solutions exist. Despite the fact that a stress state, self-balanced in the section, corresponds to these elementary solutions, they may penetrate fairly deeply and considerably change the stress–strain state pattern far from the ends. Using an asymptotic analysis of the problem, an applied theory of torsion is proposed which takes into account weakly attenuating boundary-layer solutions. |
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