This paper describes energy distribution in a block medium simulated by a one-dimensional chain of masses joined by springs and dampers. Equations describing the motion of masses are solved by the ...methods of the theory of ordinary differential equations. The effect of the block medium parameters on energy dissipation is investigated. An approximate analytical solution is obtained that describes the total energy of a block medium at large values of time.
Abstract
In the framework of the Leibenzon-Ishlinsky approach, the problem of the loss of stability of a pillar of a cylindrical mine working is solved. The pillar material was assumed with an ...initial anisotropy corresponding to the layered structure. A criterion for loss of stability is being constructed, a solution to the system of differential equations of the problem in the form of combinations of cylindrical and trigonometric functions is determined. From the fact that the determinant of a system of homogeneous algebraic equations is equal to zero, the critical load value is found at which, along with the main continuation of the deformation of the pillar, something else is possible with a changed surface geometry. The influence of the initial anisotropy, the parameters of the pillar (height, radius) on the values of the ultimate load is investigated.
It is suggested to assess plastic state of rocks around an unsupported cylindrical excavation by measured displacements of its walls. The problem (overspecified in the viewpoint of classical ...formulation) has a unique solution that allows calculation of stresses, strains and displacements in the plastic deformation domain, including the elastic-plastic boundary, without addressing the elastoplastic problem.
In order to ensure accurate hole-making in soil, it is required to adjust motion path of pneumatic puncher by deflecting its rear body relative to longitudinal axis. The structural layout of the path ...control mechanism, which allows upgrading series-production pneumatic punchers, is presented. The solution of problem on forces required to change the pneumatic puncher path in soil is given. Soil body is considered as a rigid-plastic medium, and the deflector is assumed as a nondeformable body. The problem is solved in two stages: penetration of the deflector in soil and motion of the pneumatic puncher with the rear deflected at a certain angle in soil. The loads applied to the rear for changing pneumatic puncher path in soil and the turn radius under deflecting force are determined.
The paper analyzes some of the known solutions of the problem about loading a massive body with an antiplane half-infinite crack under post-critical deformation and describes new particular ...solutions. Four boundary conditions are formulated for the interface of the elastic and post-critical deformation regions, which express continuity of two stresses and two strains. When these and other conditions are fulfilled, the solution of the problem with an infinite drop modulus behaves unusual: maximum shear stress in the vicinity of the crack tip grows infinitely rather than drops. The paper interprets the phenomenon.
The paper analyzes formulations of mathematical problems on anti-plane strains in materials under post-critical deformation. Depending on a decline modulus, the system of equilibrium equations and ...strain compatibility conditions has one or two characteristics. Given the two characteristics, finding stress-strain state of a medium needs Cauchy stress vector and displacement vector to be set at one and the same boundary. The author shows that the post-critical deformation, if included in the problem on an equilibrium semi-infinite crack, results in the infinite growth of stresses at the crack tip under unalterable deformation. Based on this, it is necessary to account for the by now disintegrated and fractured material area that is more rigid and higher modulus under the further deformation as compared with the initial state material.
Determination of a limit load in the problem of instability of rib pillars in the course of axisymmetrical bulging involves three variants of the pillar's pre-critical state: elasticity, perfect ...plasticity and post-limit deformation. The problem formulation is after Leibenzon-Ishlinskiy. The task is to find limit loads of a pillar with a pre-set dimension, such that the pillar instability is axisymmetrical.
The article offers two approaches to stress-strain state problem solution: the first is the analytical solution for the elastic deformation of a medium, the second is the numerical solution for the ...elastic and inelastic deformation. The analytical solution is based on the Kolosov-Muskhelishvili formulas, the numerical solution is analogous to the Euler solution of a regular first-order differential equation. The both methods are compared, and calculation of breaches in half-plane is exemplified.
For the case of plane strain and with Coulomb -- Mohr's criterion for rocks, the authors constructed the post-limit deformation equations that coincide in form with the plastic flow theory. It is ...shown that the system of differential equations is hyperbolic. The authors also obtained four characteristics that are nonorthogonal by symmetric relative to the first principal direction, and determined relations on the characteristics. It is found that solution of problems on failure requires that both the stress vector and displacement vectors are assigned at the contour where failure begins.
Based on the analysis of the post-limit deformation stage, it is shown that under soft loading of rocks, displacement rate greatly increases in the post-limit deformation zone, and the kinetic energy ...grows as well. It is supposed that given the kinetic energy reaches a certain threshold value, a rock block exposed to the post-limit deformation splits off the rock mass. This assumption is applied to studying the phenomenon of zonal disintegration of rocks surrounding deep cylindrical tunnels.
PDF
