On a nonstationary loading at a half-plane surface under mixed boundary conditions

Authors

  • V.D. Kubenko

DOI:

https://doi.org/10.15407/dopovidi2014.10.056

Keywords:

boundary conditions, half-plane, nonstationary loading

Abstract

The problem to determine a stressed state of the elastic half-plane under a nonstationary normal loading is considered. A mixed boundary problem is formulated, and its solution is built with using the Laplace and Fourier integral transformations. Exact inverse transforms are evaluated. As a result, the analytical solution is obtained. It determines a stress and a displacement at an arbitrary point of the half-plane at an arbitrary moment of time.

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References

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Kubenko V. D. Dopov. Nac. akad. nauk Ukr., 2011, No 10: 67–72 (in Russian).

Kubenko V. D. Usp. mekhaniki. Vols. 6th. Vol. 5, Kiev: Litera, 2009: 566–607 (in Russian).

Sneddon N., Berri D. S. Classical Theory of Elasticity, Moscow: GIFML, 1961 (in Russian).

Guz A. N., Kubenko V. D., Cherevko M. A. Diffraction of elastic waves, Kiev: Nauk. dumka, 1978 (in Russian).

Beitmen G., Erdei A. Tables of integral transforms. Vols 2. Vol 1st. Transform of Fourier, Laplace, Mellin, Moscow: Nauka, GIFML, 1969 (in Russian).

Dimkin V. A., Prudnikov A. P. ntegral transformations and operational calculus, Moscow: GIFML, 1961 (in Russian).

Beitmen G., Erdei A. Higher transcendental functions. Bessel functions, parabolic cylinder functions, orthogonal polynomials, Moscow: Nauka, 1966 (in Russian).

Published

06.03.2025

How to Cite

Kubenko, V. (2025). On a nonstationary loading at a half-plane surface under mixed boundary conditions . Reports of the National Academy of Sciences of Ukraine, (10), 56–62. https://doi.org/10.15407/dopovidi2014.10.056