Within the framework of linearized statement of the problem of elasticity theory, we study the stress-strain state of a prestrained thick plate modeled by a prestressed half space in the case of its smooth contact interaction with a rigid axisymmetric parabolic punch. The dual integral equations of this problem are solved by representing the required functions in the form of partial sums of series of Bessel functions with unknown coefficients. For their determination, we deduce finite systems of linear algebraic equations. We also analyze the influence of initial strains and the shape of the punch on the level and character of the contact stresses and vertical displacements of the boundary plane of the plate for the cases of compressible and incompressible solids. The accumulated results are illustrated for a plate with the Bartenev– Khazanovich elastic potential and with the harmonic-type potential.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 62, No. 3, pp. 113–119, July–September, 2019.
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Habrusiev, H.V., Habrusieva, І.Y. & Shelestovskyi, B.H. Contact Interaction of a Prestrained Thick Plate with Parabolic Punch. J Math Sci 263, 129–137 (2022). https://doi.org/10.1007/s10958-022-05912-x
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DOI: https://doi.org/10.1007/s10958-022-05912-x