A new method of failure analysis

Sergei Alexandrov; Marina Rynkovskaya; Ismet Bajmuratov; Ruslan Kalistratov; Ivan Pylkin

doi:10.15625/2525-2518/18622

Author affiliations

Authors

Sergei Alexandrov Ishlinsky Institute for Problems in Mechanics RAS, 101-1 Prospect Vernadskogo, Moscow 119526, Russia https://orcid.org/0000-0003-4789-6556
Marina Rynkovskaya Department of Civil Engineering, Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russia https://orcid.org/0000-0003-2206-2563
Ismet Bajmuratov Department of Civil Engineering, Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russia
Ruslan Kalistratov Department of Civil Engineering, Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russia
Ivan Pylkin Department of Civil Engineering, Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russia

DOI:

https://doi.org/10.15625/2525-2518/18622

Keywords:

linear yield criterion, plane strain, telegraph equation, failure, equations of motion in matrix forms

Abstract

The present paper develops a new failure analysis method under plane strain conditions considering a generalized linear yield criterion. The yield criterion and the stress equilibrium equations constitute a hyperbolic system of equations. It is shown that two auxiliary variables satisfy the equation of telegraphy. Simple analytical relationships connect these variables and the radii of curvature of the characteristic curves. The calculated radii of curvature allow for the corresponding characteristic net to be constructed. Then, the stress field is determined using another set of analytical relationships. Thus, a numerical procedure is only necessary for solving the equation of telegraphy. This equation can be integrated by the method of Riemann. In particular, Green’s function is the Bessel function of zero order. A simple example illustrates the general method.

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