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**A mathematical approach to solving an inverse thermoelastic problem in a thin elliptic plate.**
*(English)*
Zbl 1425.35234

Summary: This article investigates the inverse thermoelasticity of an elliptical plate for determining the temperature distribution and its associated thermal stresses by mean of integral transform techniques. Furthermore, by considering a circle as a special kind of ellipse, it is seen that the temperature distribution and history in a circular solution can be drawn as a special case of the present mathematical solution. The numerical results obtained using these computational tools are accurate enough for practical purposes.

### MSC:

35R30 | Inverse problems for PDEs |

35Q74 | PDEs in connection with mechanics of deformable solids |

74K20 | Plates |

74F05 | Thermal effects in solid mechanics |

44A10 | Laplace transform |

### Keywords:

elliptical plate; temperature distribution; thermal stresses; elliptical co-ordinate; integral transform
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\textit{I. Khan} et al., Int. J. Adv. Appl. Math. Mech. 5, No. 2, 16--24 (2017; Zbl 1425.35234)

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### References:

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