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This article is cited in 1 scientific paper (total in 1 paper)
Difference schemes of consistent approximation to stress-strain state and energy balance of medium
Yu. A. Poveshchenkoab, V. A. Gasilovab, V. O. Podrygacb, M. E. Ladonkinab, A. S. Voloshind, D. S. Boykovb, K. A. Beklemyshevad a National Research Nuclear University MEPhI
b Keldysh Institute of Applied Mathematics of RAS
c Moscow Automobile and Road Construction State Technical University (MADI)
d Moscow Institute of Physics and Technology (State University)
Abstract:
Using the support operator technique for two-dimensional problems of elasticity theory we constructed integrally consistent approximations to the components of the strain tensor and the elastic energy of the medium for the equations of the elasticity theory in terms of displacements. Approximations are constructed for the case of irregular difference grids, in the R-Z plane of a cylindrical coordinate system. We use the limiting process assuming that the azimuthal angle tends to zero for passing from the full threedimensional approximations to the two-dimensional approximations in the R-Z plane. The used technique preserves the divergent form, self-adjointness and sign-definiteness of the two-dimensional approximations. These properties are inherent in their 3D predecessors corresponding to the operators in the governing differential equations.
Keywords:
difference schemes, method of support operators, theory of elasticity, cylindrical geometry.
Received: 10.09.2018 Revised: 04.10.2018 Accepted: 19.11.2018
Citation:
Yu. A. Poveshchenko, V. A. Gasilov, V. O. Podryga, M. E. Ladonkina, A. S. Voloshin, D. S. Boykov, K. A. Beklemysheva, “Difference schemes of consistent approximation to stress-strain state and energy balance of medium”, Matem. Mod., 31:7 (2019), 3–20; Math. Models Comput. Simul., 12:2 (2020), 99–109
Linking options:
https://www.mathnet.ru/eng/mm4092 https://www.mathnet.ru/eng/mm/v31/i7/p3
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