This article is focused upon the research of smoothly adjoined shell compositions with thermo sensitive thickness in terms of Love and Reissner shell theories that differ in accuracy.The main geometric objects used to form shell compositions are torus, cone, sphere and cylinder. Examination of the generalized location vector of any point on the median surface of the composition makes it possible to determine the main curvatures and main metrical tensor components for the median surface of the composition using differential geometry methods. Three types of shell compositions are examined: open, closed and gently sloping ones. Uncoupled thermoelastic equations and natural boundary conditions are derived from the Hamilton principle in terms of displacements and rotations. Equations for temperature functions included in thermoelastic equations for shell compositions are obtained. The solution of the axisymmetric thermoelastic problem for three-element shell composition is given as an example.
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