We consider two-dimensional dynamic problems of the theory of elasticity, which can be reduced to singular integral or integrodifferential equations with immobile singularities. These problems include the problems of determination of the stressed state of bodies with edge defects and defects whose cross sections have the shape of broken line and some contact problems. For the solution of the obtained equations, we propose to apply a numerical method that takes into account the actual asymptotics of solutions and is based on the use of special quadrature formulas for singular integrals.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 1, pp. 94–105, January–March, 2020.
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Popov, V.G. Two-Dimensional Dynamic Problems of the Theory of Elasticity Reduced to Singular Integral Equations with Immobile Singularities. J Math Sci 270, 107–122 (2023). https://doi.org/10.1007/s10958-023-06335-y
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DOI: https://doi.org/10.1007/s10958-023-06335-y