A generalized Fourier method is used to solve the problem of axisymmetric indentation of a die, circular in plan, into a transversely isotropic half space with immobile paraboloidal base coaxial with the axis of the punch in the absence of friction between the punch and the half space. For this problem (regarded as an example), we perform a comparative analysis of the stress-strain state of bodies made of transversely isotropic materials with different elastic characteristics. The numerical results show that the distribution of stresses in the half space under the punch depends both on the elastic parameters and on the roots of the characteristic equation.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 4, pp. 158–162, October–December, 2013.
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Shcherbakova, Y.A. Stress-Strain State of Transversely Isotropic Half Spaces with Paraboloidal Base and Various Elastic Characteristics. J Math Sci 208, 460–466 (2015). https://doi.org/10.1007/s10958-015-2460-z
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DOI: https://doi.org/10.1007/s10958-015-2460-z