Buckling behavior of a radially loaded corrugated orthotropic thin-elliptic cylindrical shell on an elastic foundation

• A new structural model for the buckling of elliptic cylindrical shells is offered.
• A new approach for solving a three-dimension boundary-value problem is presented.
• A new function of corrugation in the hoop direction of the shell is presented.

This paper is aimed to investigate how the corrugation parameters and the Winkler foundation affect the buckling behavior of isotropic and orthotropic thin-elliptic cylindrical shells with cosine-shaped meridian subjected to radial loads. The buckling three-dimensional equations of the shell are amended by including the Winkler foundation modulus based on the Flügge thin shell theory and Fourier's approach is used to deform the displacement fields as trigonometric functions in the longitudinal direction of shell. Using the transfer matrix of the shell, the governing equations of buckling can be written in a matrix differential equation of variable coefficients as a one-dimensional boundary-value problem that is solved numerically as an initial-value problem by the Romberg integration approach. The proposed model is adopted to determine the basic loads and the corresponding buckling deformations for the symmetrical and antisymmetrical modes of buckling. The sensitivity of the buckling behavior and bending deformations to the corrugation parameters, Winkler foundation moduli, ellipticity and orthotropy of the shell structure is studied for different type-modes of buckling. The obtained results indicate that this design model allows us to find out how the local properties of the shell and its stiffness in existence of an elastic foundation are related and would serve as benchmarks for future works in this important area.