Abstract
The article deals with a method for solving a dynamic problem of the theory of elasticity. According to this method, the stresses and momentums forming a single four-dimensional (4D) tensor are considered to be unknown. The formulation of the basic relations of the theory of elasticity in 4D space is given. As an example, the problem of the ball oscillations under the action of bulk forces is analyzed.
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References
N. A. Kilchevsky, Elements of Tensor Calculus and its Application in Mechanics (Naukova Dumka, Kiev, 1972) [in Russian].
W. Nowacki, Theory of Elasticity (Mir, Moscow, 1975) [in Russian].
A. G. Gorshkov, A. L. Medvedskii, L. N. Rabinskii, and D. V. Tarlakovskii, Waves in Continuous Media (Fizmatlit, Moscow, 2004) [in Russian].
P.K. Rashevsky, Riemannian Geometry and Tensor Analysis (Nauka, Moscow, 1976) [in Russian].
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Original Russian Text © L.V. Fedorov, 2018, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2018, No. 6, pp. 13–20.
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Fedorov, L.V. Solution of the Dynamic Problem of the Linear Theory of Elasticity. Mech. Solids 53, 609–614 (2018). https://doi.org/10.3103/S002565441806002X
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DOI: https://doi.org/10.3103/S002565441806002X