Determination of stresses in concrete lining with rock-bolt in case of exhaustion of rock-bolt supporting strength

The article deals with the solution of analytical problem of flat axisymmetric elasticity theory, when rock-bolt supporting strength is exhausted. Expression for determination of stresses in concrete lining is deduced, where pressure increasing at exploitation have regarded. This methodology can be used at blueprint stage and preliminary calculation during mining operations. Further evaluation of concrete lining strength and geophysical probe of rock is needed for the preliminary calculation.

Axisymmetric elasticity solution for an undrained saturated poro-piezoelastic thick disk

In this paper, a circular thick plate made of poroelastic piezoelectric ceramic is studied. The porosities of the plate vary through the thickness and axisymmetric behavior of a piezoelectric disk exhibiting hexagonal material symmetry of class 6 mm. Additionally, external mechanical loads which are in axi-symmetric general form act on the plate. The material properties of the plate vary exponentially as functions of the ?? variable in cylindrical coordinates. Based on an elasticity solution in terms of radial and axial displacements (??, ??), the governing partial differential equations are derived and solved analytically; mechanical stresses and electric displacements are then calculated. Finally an example which illustrates the application of the derived formulas is presented.

Cosserat Spectrum of an Axisymmetric Elasticity Problem for a Finite-Length Solid Cylinder

ABSTRACTAn algorithm for the computation and analysis of the Cosserat spectrum for an axisymmetric elasticity boundary-value problem in a finite-length solid cylinder with boundary conditions in terms of stresses is proposed. By making use of the cross-wise superposition method, the spectral problem is reduced to systems of linear algebraic equations. A solution method for the mentioned systems is presented and the asymptotic behavior of the Cosserat eigenvalues is established. On this basis, the key features of the Cosserat spectrum for the mentioned problem are analyzed with special attention given to the effect of the cylinder aspect ratio.