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.


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
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