• Geomechanics and Engineering
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• v.24 no.3
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• pp.227-235
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• 2021

A criterion and a method for solving a problem on the prevention of mine working fracture under the action of tectonic and gravitational forces are offered. Based on minimal criterion, theoretical analysis of the definition of the optimal shape of working in the rock mass weakened by arbitrarily located rectilinear cracks was carried out. A closed system of algebraic equations allowing to minimize the stress state and stress intensity factors depending on mechanical and geometrical characteristics of the rock, is constructed. The relation between the shape of the working and the stress intensity factors and also location and sizes of the cracks is obtained. The found optimal shape of working increases load-bearing capacity of the rock.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.6
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• pp.969-980
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• 2003

The interactions between curved cracks are examined in an orthotropic plate and the effects of rectilinear anisotropy on the stress intensity factors are analyzed. The finite element alternating method (FEAM) is used in this study to get the stress intensity factors for the multiple curved cracks. To obtain analytical solutions, which is necessary in FEAM, the curved cracks are modeled as continuous distributions of dislocations, and integral equations are formulated for unknown dislocation density functions to satisfy the given resultant forces on the crack surfaces. Several basic problems are solved to verify the accuracy and efficiency of the proposed method and it can be found that present results show good agreements with the previously published results.

• Structural Engineering and Mechanics
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• v.73 no.5
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• pp.585-598
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• 2020

We develop design model within which nucleation and propagation of crack in a fibrous composite is described. It is assumed that under loading, crack initiation and fracture of material happens in the composite. The problem of equilibrium of a composite with embryonic crack is reduced to the solution of the system of nonlinear singular integral equations with the Cauchy type kernel. Normal and tangential forces in the crack nucleation zone are determined from the solution of this system of equations. The crack appearance conditions in the composite are formed with regard to criterion of ultimate stretching of the material's bonds. We study the case when near the fiber, the binder has several arbitrary arranged rectilinear prefracture zones and a crack with interfacial bonds. The proposed computational model allows one to obtain the size and location of the zones of damages (prefracture zones) depending on geometric and mechanical characteristics of the fibrous composite and applied external load. Based on the suggested design model that takes into account the existence of damages (the zones of weakened interparticle bonds of the material) and cracks with end zones in the composite, we worked out a method for calculating the parameters of the composite, at which crack nucleation and crack growth occurs.