Igor V. Yanchevsky

Bio: Igor V. Yanchevsky is an academic researcher from National Academy of Sciences of Ukraine. The author has contributed to research in topics: Two-sided Laplace transform & Laplace transform applied to differential equations. The author has an hindex of 1, co-authored 1 publications receiving 2 citations.

Nonstationary distributed axisymmetric load on an elastic half-space

Abstract: This paper presents analytical and numerical-analytic approaches to solving the problem of the action of an arbitrarily distributed axisymmetric load applied instantly to the surface of an isotropic elastic half-space. The first approach is built around the Laplace and Hankel integral transforms whose inversion is performed jointly with Cagniard’s technique, and as a result, exact analytical expressions are obtained for computing stresses along an axis of symmetry. The second approach uses the Laplace integral transform and the expansion of sought for values into the Fourier–Bessel series to reduce the problem to a numerical solution of a series of Volterra integral equations. Concrete numerical analysis was performed for cases where the domain of application of a distributed load is fixed or expands in time with both constant and variable velocity.

Nonsteady Problem for an Elastic Half-Plane with Mixed Boundary Conditions

Abstract: An approach to studying nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed. The Laplace and Fourier transforms are used. The sequential inversion of these transforms or the inversion of the joint transform by the Cagniard method allows obtaining the required solution (stresses, displacements) in a closed analytic form. With this approach, the problem can be solved for various types of loads