The Stressed State of the “Boundary Layer” Type in Cylindrical Shells Investigated according to a Nonclassical Theory

Abstract

Two variants of a refined theory for calculating the stress–strain state in the boundary zones of cylindrical shells are presented. The relevant mathematical models are based on equations of the three-dimensional elasticity theory and the increase over the thickness of the shell in the orders of the polynomials that approximate the sought displacements. The Lagrange variational principle is applied to the value of the shell’s total energy functional defined more exactly with respect to the classical Kirchhoff–Love theory. The formulated boundary problems allow determination with different degrees of accuracy of additional stressed states of the “boundary layer” type. The calculated results obtained in this work are compared with the results obtained according to the classical theory. It has been established that the above stresses make a significant contribution to the total stressed state of the shell and should be considered when designing and testing machine structures for strength and longevity.