For rectangular layered shallow cylindrical shells of irregular structure, the quasi-static problem of unbound thermoelasticity is formulated. As a mathematical model, the equations of the shear theory of shallow shells of Timoshenko type are used. The closed solution for the formulated problem is found by the methods of integral transformations. The distribution of temperature, displacements, forces and moments in a two-layer cylindrical shell under local convective heating is analyzed numerically.
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