Abstract:
It is proved that the solutions of the static equations of a continuous medium constructed in terms of a stress function are self-equilibrated. From a mathematical point of view, these functions can be treated as the connectivity coefficients of the intrinsic geometry of the medium. It is shown that from a physical point of view, the existence of self-equilibrated stress fields is due to a nonuniform entropy distribution in the medium. As an example, for a circle in polar coordinates and a cylindrical sample, a self-equilibrated stress field and an elastic field compensating for its surface component are constructed and it is shown how to write the equation for the intrinsic geometrical characteristics.
Citation:
V. P. Myasnikov, M. A. Guzev, A. A. Ushakov, “Self-equilibrated stress fields in a continuous medium”, Prikl. Mekh. Tekh. Fiz., 45:4 (2004), 121–130; J. Appl. Mech. Tech. Phys., 45:4 (2004), 558–566
This publication is cited in the following 5 articles:
V.V. Makarov, M.A. Guzev, V.N. Odintsev, “Development of Geomechanics of Highly Compressed Rocks and Rock Masses in Russia”, Geohazard Mechanics, 2025
M. A. Guzev, W. Liu, Ch. Qi, E. P. Riabokon, “Compensating role self-balanced stress fields in constructing nonsingular solutions using a non-Euclidean model of a continuous medium for an incompressible sphere”, J. Appl. Mech. Tech. Phys., 62:5 (2021), 736–741
Mikhail A. Guzev, Modeling in Geotechnical Engineering, 2021, 61
S. N. Aristov, I. E. Keller, “Beltrami stress fields in an elastic body”, Dokl. Phys., 61:7 (2016), 343
M. A. Guzev, “Structure of kinematic and force fields in the Riemannian continuum model”, J. Appl. Mech. Tech. Phys., 52:5 (2011), 709–716
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