We reduce the problem of thermoviscoelasticity for a piecewise homogeneous plate to a recurrence sequence of thermoelasticity problems by the method of small parameter with the use of generalized complex potentials. In the obtained solution, all quantities depend on the powers of the small parameter, the replacement of which by an operator expression enables us to find stresses at any moment of time. We present an analytic solution of the problem for a plate with a single inclusion and describe results of numerical investigations.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 55, No. 2, pp. 131–143, April–June, 2012.
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Kaloerov, S.A., Petrenko, O.A. Problem of thermoviscoelasticity for a piecewise homogeneous anisotropic plate. J Math Sci 192, 634–649 (2013). https://doi.org/10.1007/s10958-013-1422-6
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DOI: https://doi.org/10.1007/s10958-013-1422-6