8. Fractional Thermoelasticity of Thin Shells

The notion of a thin shell (a solid with one size being small with respect to two other sizes) allows reducing of a three-dimensional problem to a two-dimensional one for the median surface. In such an approach, investigation of thermomechanical state of a considered three-dimensional solid is reduced to investigation of thermomechanical state of the median surface endowed with equivalent properties characterizing deformation and heat conduction. Equations of fractional thermoelasticity of thin shells are formulated for theories based on the time-fractional heat conduction equation as well as on the time-fractional telegraph equation. The generalized boundary conditions of nonperfect thermal contact for the time-fractional heat conduction in composite medium are also obtained. These boundary conditions take into account the reduced heat capacity, reduced thermal conductivity and reduced thermal resistance of the median surface modeling the transition region between solids in contact.