Yuri Antipov | Louisiana State University (original) (raw)

Papers by Yuri Antipov

International Journal of Fracture, 1997

In the present paper two contact problems referring to the partially stiffened elastic half-plane... more In the present paper two contact problems referring to the partially stiffened elastic half-plane along its edge with a reinforcement (or stringer) either in the form of a rigid plate or a smooth rigid stamp, are considered. The half-plane contains an edge crack which is arbitrarily pressurized, and is perpendicular to the bounding edge of the half-space. It is assumed that the mid-point of the stringer is located in the axis of the crack. Each of the above two half-plane contact problems is first reduced to a system of two singular integral equations with fixed singularities. Then by employing the generalized method of integral transforms, this system is further reduced to a system of Wiener–Hopf equations that is equivalent to the Riemann matrix boundary value problem. Exact analytical solutions of the two problems are presented in series form. Asymptotic approximations for the stress intensity factor and the energy release rate at the crack tip are also given. Finally, numerical results for the contact stresses, crack opening displacements, stress intensity factor and crack energy are displayed.

International Journal of Fracture, 1997

The plane strain elastic half-plane problem of an edge crack lying along the interface of two per... more The plane strain elastic half-plane problem of an edge crack lying along the interface of two perfectly bonded dissimilar quarter-planes is considered. Moreover, on the boundaries of the two quarter-planes concentrated forces are acting. For the correct formulation of the crack problem at hand, we consider the existence of a small slippage zone near the crack tip where closing stresses act. The mixed boundary value problem is subsequently reduced to a system of two functional equations of the Wiener–Hopf type which are effectively solved. The exact analytical solution of the problem is presented in series form. Numerical results, as well as asymptotic solutions for the most important physical quantities, are also presented. It is shown that there exist certain modes of surface loading of the homogeneous half-space, that result to the formation of two distinct zones at the crack tip region, one where the crack opening occurs and another adjacent to it, where frictionless contact of crack lips takes place. Also, it is demonstrated that in the case of high contrast of Young's moduli of the two quarter-planes, two opening-contact intervals appear consecutively along the crack.

The problem for a one non-symmetric supercavitating wedge in a jet is considered. The single- and... more The problem for a one non-symmetric supercavitating wedge in a jet is considered. The single- and double-spiral-vortex models proposed by Tulin are used to describe the flow of the liquid at the rear part of the cavity. Both problems are solved in a closed form using the methods of complex analysis. The models are compared with respect to different parameters of the flow. It is obtained that the flow around the wedge, in the front part of the cavity and the lift and drag coefficients are not affected by the choice of the model. On the other hand, the flow at the tail part of the cavity and the length of the cavity depend strongly on the chosen model.

Journal of Engineering Mathematics, 2007

A solution for a crack propagating under shear loading in an isotropic viscoelastic medium with d... more A solution for a crack propagating under shear loading in an isotropic viscoelastic medium with different relaxation under volume and shear deformations is presented. The medium is infinite and the semi-infinite crack propagates along the x1-axis at constant speed V , which may take any value up to the speed of dilatational waves. The requisite Riemann-Hilbert problem for the steady-state case has been solved and the asymptotics of the stress component σ12 directly ahead of the crack and at infinity have been obtained. * Partial support by Louisiana Board of Regents grant LEQSF(2005-07)-ENH-TR-09 is acknowledged.

Journal d'Analyse Mathématique, 2012

Abstract. The following problem arises in thermoacoustic tomography and has intimate connection w... more Abstract. The following problem arises in thermoacoustic tomography and has intimate connection with PDEs and integral geometry: Reconstruct a function f supported in an n-dimensional ball B, if the spherical means of f are known over all geodesic spheres ...

Arxiv preprint arXiv:1107.5992, Jan 1, 2011

The work develops further the theory of the following inversion problem, which plays the central ... more The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: Reconstruct a function f supported in an n-dimensional ball B, if the spherical means of f are known over all geodesic spheres centered on the boundary of B. We propose a new unified approach based on the idea of analytic continuation. This approach gives explicit inversion formulas not only for the Euclidean space R n (as in the original set-up) but also for arbitrary constant curvature space X, including the n-dimensional sphere and the hyperbolic space. The results are applied to inverse problems for a large class of Euler-Poisson-Darboux equations in constant curvature spaces of arbitrary dimension.

International Journal of Fracture, 1997

In the present paper two contact problems referring to the partially stiffened elastic half-plane... more In the present paper two contact problems referring to the partially stiffened elastic half-plane along its edge with a reinforcement (or stringer) either in the form of a rigid plate or a smooth rigid stamp, are considered. The half-plane contains an edge crack which is arbitrarily pressurized, and is perpendicular to the bounding edge of the half-space. It is assumed that the mid-point of the stringer is located in the axis of the crack. Each of the above two half-plane contact problems is first reduced to a system of two singular integral equations with fixed singularities. Then by employing the generalized method of integral transforms, this system is further reduced to a system of Wiener–Hopf equations that is equivalent to the Riemann matrix boundary value problem. Exact analytical solutions of the two problems are presented in series form. Asymptotic approximations for the stress intensity factor and the energy release rate at the crack tip are also given. Finally, numerical results for the contact stresses, crack opening displacements, stress intensity factor and crack energy are displayed.

International Journal of Fracture, 1997

The plane strain elastic half-plane problem of an edge crack lying along the interface of two per... more The plane strain elastic half-plane problem of an edge crack lying along the interface of two perfectly bonded dissimilar quarter-planes is considered. Moreover, on the boundaries of the two quarter-planes concentrated forces are acting. For the correct formulation of the crack problem at hand, we consider the existence of a small slippage zone near the crack tip where closing stresses act. The mixed boundary value problem is subsequently reduced to a system of two functional equations of the Wiener–Hopf type which are effectively solved. The exact analytical solution of the problem is presented in series form. Numerical results, as well as asymptotic solutions for the most important physical quantities, are also presented. It is shown that there exist certain modes of surface loading of the homogeneous half-space, that result to the formation of two distinct zones at the crack tip region, one where the crack opening occurs and another adjacent to it, where frictionless contact of crack lips takes place. Also, it is demonstrated that in the case of high contrast of Young's moduli of the two quarter-planes, two opening-contact intervals appear consecutively along the crack.

The problem for a one non-symmetric supercavitating wedge in a jet is considered. The single- and... more The problem for a one non-symmetric supercavitating wedge in a jet is considered. The single- and double-spiral-vortex models proposed by Tulin are used to describe the flow of the liquid at the rear part of the cavity. Both problems are solved in a closed form using the methods of complex analysis. The models are compared with respect to different parameters of the flow. It is obtained that the flow around the wedge, in the front part of the cavity and the lift and drag coefficients are not affected by the choice of the model. On the other hand, the flow at the tail part of the cavity and the length of the cavity depend strongly on the chosen model.

Journal of Engineering Mathematics, 2007

A solution for a crack propagating under shear loading in an isotropic viscoelastic medium with d... more A solution for a crack propagating under shear loading in an isotropic viscoelastic medium with different relaxation under volume and shear deformations is presented. The medium is infinite and the semi-infinite crack propagates along the x1-axis at constant speed V , which may take any value up to the speed of dilatational waves. The requisite Riemann-Hilbert problem for the steady-state case has been solved and the asymptotics of the stress component σ12 directly ahead of the crack and at infinity have been obtained. * Partial support by Louisiana Board of Regents grant LEQSF(2005-07)-ENH-TR-09 is acknowledged.

Journal d'Analyse Mathématique, 2012

Abstract. The following problem arises in thermoacoustic tomography and has intimate connection w... more Abstract. The following problem arises in thermoacoustic tomography and has intimate connection with PDEs and integral geometry: Reconstruct a function f supported in an n-dimensional ball B, if the spherical means of f are known over all geodesic spheres ...

Arxiv preprint arXiv:1107.5992, Jan 1, 2011

The work develops further the theory of the following inversion problem, which plays the central ... more The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: Reconstruct a function f supported in an n-dimensional ball B, if the spherical means of f are known over all geodesic spheres centered on the boundary of B. We propose a new unified approach based on the idea of analytic continuation. This approach gives explicit inversion formulas not only for the Euclidean space R n (as in the original set-up) but also for arbitrary constant curvature space X, including the n-dimensional sphere and the hyperbolic space. The results are applied to inverse problems for a large class of Euler-Poisson-Darboux equations in constant curvature spaces of arbitrary dimension.