Publication: Difference Schemes of Consistent Approximation of the Stress-Strain State and Energy Balance of a Medium
Дата
2020
Авторы
Podryga, V. O.
Ladonkina, M. E.
Voloshin, A. S.
Boykov, D. S.
Poveshchenko, Y. A.
Gasilov, V. A.
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© 2020, Pleiades Publishing, Ltd.Abstract: Using the support operator technique for two-dimensional problems of the elasticity theory we constructed integrally consistent approximations of 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 three-dimensional 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.
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Difference Schemes of Consistent Approximation of the Stress-Strain State and Energy Balance of a Medium / Podryga, V.O. [et al.] // Mathematical Models and Computer Simulations. - 2020. - 12. - № 2. - P. 99-109. - 10.1134/S2070048220020131