The previously developed general asymptotic theory of thin multilayer shells is used for the case of cylindrical shells. The ratios are presented in explicit analytical form for all six components of the stress tensor in a thin multilayer elastic cylindrical shell, depending on the deformations, curvatures of the middle surface of the shell, as well as their derivatives along the longitudinal coordinates. The obtained formulas make it possible to calculate all the distributions of the components of the stress tensor over the thickness in a cylindrical shell after finding solutions to the two-dimensional problem of the theory of KirchhoffLyav shells. An example is given of the calculation of stresses in a cylindrical composite shell underaxisymmetric bending by pressure. To calculate stresses by these formulas, only a differentiation of displacements is required - a deflection and two displacements of the middle surface of the shell, for which an analytical solution is obtained.
Димитриенко Ю.И., Губарева Е.А., Пичугина А.Е. Моделирование напряжений в тонких композитных цилиндрических оболочках на основе асимптотической теории. Математическое моделирование и численные методы, 2018, № 3, с. 114–132.