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Hits: 367

Authors: O. Z. NAMAZOV, R. M. TAGIYEV

Keywords: gas-lift, hyperbolic equation,differential equation,relaxation method,integral equation

DOI:  https://doi.org/10.32010/j.bmj.2022.16

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Hits: 349

Authors: A. R. SAGITOVA, A. V. SHAKIROVA, Ya. T. SULTANAEV

Keywords: Sturm--Liouville equation, asymptotics of solutions, oscillating potential, Hausdorff identity

DOI:  https://doi.org/10.32010/j.bmj.2022.15

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Hits: 380

Authors: M. E. KERIMOVA, M. M. SABZALIYEV

Abstract. A boundary value problem stated in an infinite semi-strip for a third order non-classic type differential equation degenerated  into a hyperbolic equation,  is considered. The complete expansion of the solution of the  problem with respect to a small parameter as constructed and the residual term is estimated.

Keywords: boundary value problem, non-classic type differential equation, hyperbolic equation, small parameter, boundary layer type function, residual term

DOI:  https://doi.org/10.32010/j.bmj.2022.14

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Hits: 378

Authors: A. K. MEKHDIEV, R. K. MEKHTIEV

Abstract. 

An elastic medium is considered, weakened by a doubly periodic system of round holes, filled with absolutely rigid inclusions, soldered along the bypass and has a crack initiation. The medium (binder) is weakened by two periodic systems of rectilinear crack initiation directed collinear to the abscissa and ordinate axes, and their sizes are not the same. General representations are constructed that describe a class of problems with a doubly periodic stress distribution outside circular holes and cracks under transverse shear. The analysis of the limiting equilibrium of cracks in the framework of the end zone model is carried out on the basis of a nonlocal fracture criterion with a force condition for the propagation of the crack tip and a deformation condition for determining the advancement of the edge of the end zone of the crack.

Basic resolving equations are obtained in the form of infinite algebraic systems and three nonlinear singular integro-differential equations.

The equations in each approximation were solved by the Gaussian method with the choice of the principal element for different values of the order of M, depending on the radius of the holes. Calculations were carried out to determine the forces in the connections of the end zones and the ultimate loads causing the growth of cracks.

Keywords: doubly periodic lattice, average stresses, boundary conditions, transverse shear, linear algebraic equations, singular equations, crack initiation

DOI:  https://doi.org/10.32010/j.bmj.2022.13