Studying stiffened shells stress state by the refined theory with account for ribs elasticity and clamped edge
The presented article considers the clamped edge pliability and ribs stiffness impact on the stress state of stiffened shells determined by the refined theory. Computing was performed according to the approach based on the shell displacement expanding into polynomials, one degree higher than the classical theory of Kirchhoff-Love type, over the coordinate normal to the median surface. Differential equation of equilibrium and boundary conditions of the shell were obtained based on the 3D theory of elasticity and Lagrange variation principle. The formulated boundary problem was solved by an analytical method using the Laplace transform. The calculation results revealed quickly damping additional stress states of the “boundary layer” type while calculations were performed by the refined theory. The values of longitudinal and circumferential shell stresses are substantially refined nearby the stress state distortion zones (in places of ribs fixing and clamped edge), while normal stresses values are of the same order with maximum values of the main (internal) stress. The study revealed that the shell stresses reduced several times with account for the clamped edge pliability. An important result related to the additional stress state consists in the fact that with the ribs stiffness increases, the transverse normal stresses, neglected in the classical theory, increase substantially. The obtained results can be applied for the design and evaluation of the strength of aircraft stiffened shells