##
**A plane dynamical problem of coupled electroelasticity.**
*(Russian, English)*
Zbl 1183.74092

Prikl. Mat. Mekh. 72, No. 5, 842-851 (2008); translation in J. Appl. Math. Mech. 72, No. 5, 611-618 (2008).

The authors discuss a method for the solution of two-dimensional internal and external boundary-value problems of coupled electroelasticity with allowance for finite velocity of propagation of thermal impulses. The method is based on the construction of fundamental solutions to appropriate equations. In the framework of the stated problems, coupling of thermomechanical fields is estimated and hyperbolic and parabolic heat conductivity models are compared.

Reviewer: Ju. N. Shevchenko (Kyïv)

### MSC:

74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |

74F05 | Thermal effects in solid mechanics |

PDF
BibTeX
XML
Cite

\textit{V. N. Kobzar'} and \textit{L. A. Fil'shtinsky}, Prikl. Mat. Mekh. 72, No. 5, 842--851 (2008; Zbl 1183.74092); translation in J. Appl. Math. Mech. 72, No. 5, 611--618 (2008)

### References:

[1] | Danilovskaya, V. I.: Thermal stresses in an elastic half-space due to abrupt heating of its boundary, Prikl mat mekh 14, No. 3, 316-318 (1950) |

[2] | Kartashov, E. M.; Parton, V. Z.: Dynamic thermoelasticity and thermal shock problems. Advances in science and technology, Mechanics of a deformable solid. Moscow: VINITI 22, 55-127 (1991) |

[3] | Fil’shtinskii, L. A.; Yu, V. Sirenko: Two-dimensional fundamental solutions in the coupled problem of thermoelasticity, Teor prikl mekh 37, 157-161 (2003) |

[4] | Nowacki, W.: Dynamic problems of thermoelasticity, (1966) · Zbl 0203.27702 |

[5] | Gribanov, V. F.; Panichkin, N. G.: Coupled and dynamic problems of thermoelasticity, (1984) · Zbl 0452.73097 |

[6] | Boley, B. A.; Weiner, J. H.: Theory of thermal stresses, (1960) · Zbl 0095.18407 |

[7] | Vladimirov, V. S.: The equations of mathematical physics, (1981) · Zbl 0699.53073 |

[8] | Belotserkovskii, S. M.; Lifanov, I. K.: Numerical methods in singular integral equations and their application in aerodynamics, elasticity and electrodynamics, (1985) · Zbl 0578.65140 |

[9] | Babolian, E.; Biazar, J.; Vahidi, A. R.: A new computational method for Laplace transforms by decomposition method, Appl math comput 150, No. 3, 841-846 (2000) · Zbl 1039.65094 |

[10] | Abate, J.; Choudhury, G. L.; Witt, W.: W.grassmanan introduction to numerical transform inversion and its application to probability models, computational probability, An introduction to numerical transform inversion and its application to probability models, computational probability, 257-323 (1999) · Zbl 0945.65008 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.