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Inhomogeneous Problem of the Theory of Elasticity in a Half-Strip. Exact Solution

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Abstract—

In the paper, in the form of series in the Papkovich–Fadle eigenfunctions, exact solutions of two inhomogeneous boundary value problems of elasticity theory for a half-strip with free long sides are constructed: (1) the half-strip end is free, (2) the half-strip end is rigidly clamped. To solve the inhomogeneous problem in a free strip, the Papkovich orthogonality relation is used. The exact solution for the half-strip is then added to it.

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Notes

  1. Similar equations describing the solution of the homogeneous problem for a half-strip were obtained in [8], but for an odd-symmetric deformation of the half-strip.

REFERENCES

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Funding

Research by M.D. Kovalenko and I.V. Menshova (Sections 3 and 4) was carried out with the financial support of the Russian Foundation for Basic Research and the National Natural Science Foundation of China within the framework of scientific project no. 20-51-53021. Research by A.P. Kerzhaev (Sections 1 and 2) was supported by a grant from the Russian Science Foundation (project no. 19-71-00094). The research of G. Yu was funded by the National Natural Science Foundation of China (no. 51674150) and NSFC-RFBR (no. 5191101589).

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Authors and Affiliations

  1. Institute of Earthquake Prediction Theory and Mathematical Geophysics of RAS, 117997, Moscow, Russia

    M. D. Kovalenko, I. V. Menshova & A. P. Kerzhaev

  2. Institute of Applied Mechanics of Russian Academy of Sciences, 125040, Moscow, Russia

    M. D. Kovalenko

  3. Bauman Moscow State Technical University, 105005, Moscow, Russia

    I. V. Menshova

  4. School of Civil Engineering, Qingdao University of Technology, Qingdao, China

    G. Yu

  5. Cooperative Innovation Center of Engineering Construction and Safety in Shandong Blue Economic Zone, Qingdao University of Technology, Qingdao, China

    G. Yu

Authors
  1. M. D. Kovalenko
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  2. I. V. Menshova
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  3. A. P. Kerzhaev
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  4. G. Yu
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Corresponding authors

Correspondence to M. D. Kovalenko, I. V. Menshova, A. P. Kerzhaev or G. Yu.

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Translated by M. Katuev

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Kovalenko, M.D., Menshova, I.V., Kerzhaev, A.P. et al. Inhomogeneous Problem of the Theory of Elasticity in a Half-Strip. Exact Solution. Mech. Solids 55, 784–790 (2020). https://doi.org/10.3103/S0025654420060096

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  • DOI: https://doi.org/10.3103/S0025654420060096

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