The general asymptotic theory of thin multilayer shells developed by the authors earlier in Part 1 of this study is applied to cylindrical anisotropic thermoelastic shells. It is shown that for cylindrical shells the general theory is substantially simplified: general two-dimensional averaged thermoelasticity equations for multilayer shells are obtained. These equations are similar to the classical equations of cylindrical shells in the Kirchhoff-Love theory, but they are obtained in a completely different way: on the basis of only an asymptotic analysis of the general three-dimensional equations of the theory of thermoelasticity. No hypotheses regarding the distribution of displacements or stresses over the thickness are used in this theory, which makes it logically consistent. In addition, the developed theory makes it possible to obtain explicit analytical expressions for all 6 components of the stress tensor in cylindrical anisotropic shells. Explicit expressions are obtained for all tensor constants included in these stress formulas. An example of calculating thermal stresses in a cylindrical composite shell with axisymmetric bending due to the combined action of external pressure and one-sided non-stationary heating is given. An example of a layered-fiber 4-layer shell with different angles of helical winding of reinforcing fibers is considered. It is shown that the developed one allows one to study in detail such complex effects as the formation of significant transverse thermal stresses during heating, which significantly exceed the level of interlayer shear stresses, which are traditionally considered the most dangerous for layered composites.
Димитриенко Ю.И., Губарева Е.А., Пичугина А.Е., Белькова К.В., Борин Д.М. Моделирование термонапряжений в композитных оболочках на основе асимптотической теории. Часть 2. Расчет цилиндрических оболочек. Математическое моделирование и численные методы, 2022, № 3, с. 3–30