Выпуск 4(10), 2017

Видеоматериалы

Архив

S. E. Alexandrov, E. A. Lyamina

A NEW METHOD OF CALCULATING THE STATE OF STRESS
IN GRANULAR MATERIALS UNDER PLANE STRAIN CONDITIONS

Data of reciept 01.10.2017
Decision on publication 26.10.2017

The system of equations comprising the Mohr-Coulomb yield condition and the stress equi-
librium equations may be studied independently of the flow law. This system of equations is hy-
perbolic. Accordingly, to solve the aforementioned system of equations, it is reasonable to apply
the method of characteristics. In the special case of plasticity theory for materials whose yield cri-
terion does not depend on the average stress, two methods are used to construct an orthogonal net
of characteristics and to determine the stress field: the R-S method and Mikhlin’s coordinate
method. In the case of the Mohr-Coulomb yield condition, the angle between the characteristic
directions depends on the internal friction angle. Therefore, the above-mentioned methods should
be generalised in accordance with this property of characteristics.
Purpose. In the case of Plasticity theory for materials whose yield strength does not de-
pend on the average stress, to calculate the stress filed, Mikhlin’s coordinate method is widely
used. The purpose of this study is to generalise this method for the equation system consisting
of the Mohr-Coulomb yield criterion and the pressure equilibrium equations.
Methods. The geometrical properties of the characteristics of the equations’ system
consisting of the Mohr-Coulomb yield condition and the equilibrium equations are used to
introduce the generalised Mikhlin coordinates.
Results. It’s been pointed out that solving equation system consisting of the Mohr-
Coulomb yield condition and equilibrium equation comes to solving equation of telegraphy
and to subsequent integration.
Practical Significance. The developed method of system of equations’ solution, con-
sisting of the Mohr-Coulomb yield condition and equilibrium equation enables obtaining high
precision solutions at insignificant computer time expenditures.

Mohr-Coulomb yield condition, method of characteristics, Mikhlin’s variables, equation
of telegraphy.