Geodesic
Difference schemes of consistent approximation to stress-strain state and energy balance of medium
Matematičeskoe modelirovanie, Tome 31 (2019) no. 7, pp. 3-20

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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. 
@article{MM_2019_31_7_a0,
     author = {Yu. A. Poveshchenko and V. A. Gasilov and V. O. Podryga and M. E. Ladonkina and A. S. Voloshin and D. S. Boykov and K. A. Beklemysheva},
     title = {Difference schemes of consistent approximation to stress-strain state and energy balance of medium},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--20},
     publisher = {mathdoc},
     volume = {31},
     number = {7},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2019_31_7_a0/}
}
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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. Matematičeskoe modelirovanie, Tome 31 (2019) no. 7, pp. 3-20. http://geodesic.mathdoc.fr/item/MM_2019_31_7_a0/