The study of the longitudinally stiffened cylindrical shells under action of local load by the refined theory

Dynamics, strength of machines, instruments and equipment


Firsanov V. V.*, Vo A. H.**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



At present, engineering calculations of ribbed shells are based on the results of the classical theory of Kirchhoff-Love and Timoshenko-Reissner type. The hypotheses adopted in this theory does not allow accounting for the shell transverse deformations, leading to the errors in the determining the stress-strain state (SSS). It forces to develop increasingly advanced methods for SSS calculating with account for the distortion zones, including those near the joints of structural elements, as well as local loading.

The purpose of this article consists in developing a refined version of the theory of the SSS calculating of longitudinally stiffened cylindrical shells under the impact of radial axisymmetric local load.

The shell displacements are approximated by high degree polynomials with respect to the classical theory of Kirchhoff-Love and Timoshenko-Reissner type. Basic equations and boundary conditions obtained by the minimum total energy of deformation principle are presented. The boundary value problem solution is performed by operational method based on the Laplace transform.

The results obtained in this article allowed establish that the with the ribbed shell calculation by the refined theory there were always rapidly damped additional edge stress states of the “interface” type. Near distortion zones of the stressed state, the transverse normal stresses, neglected in the classical theory, were obtained of the same order with the maximum values of the basic flexural stress. Moreover, for the thicker shells the transverse normal stresses contribution to the total SSS increases significantly.


stiffened shells, refined theory, stress state “boundary layer”, local load, Lagrange principle, the Laplace transform, transverse normal stresses


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