Buckling of Thin-Walled Cylindrical Shell Structures with Axially Variable Elastic Modulus Under Axial Compression

This paper conducts the analytical investigation on the buckling of cylindrical shells with axially variable elastic modulus subjected to axial compressive load for the first time. First, it proves that the axially distributed elastic modulus can be expressed as the combination of constant and variable component. Then, governing differential equations for buckling analysis are derived and exactly solved by the combined perturbation method and Fourier analysis. Accordingly, the closed analytical solutions for the cylinder with arbitrarily variable elastic modulus are obtained, which reveal the explicit relations among buckling load, shell sizes and elastic modulus functions. Based on the presented analytical formulas, four types of elastic modulus variations for shell material which are uniform, periodic, linear and combined are studied in detail, and the results are also well verified. The derived analytical solutions in this paper can serve as benchmarks for buckling analyses of thin-walled cylinders with elastic modulus variations resulted from design, material manufacturing process, material imperfections and so on.

Automated summary

This paper analytically investigates the buckling behavior of cylindrical shells with axial variable elastic modulus under axial compressive load for the first time. The distributed elastic modulus is expressed as a combination of constant and variable components. Governing differential equations are derived and solved using the combined perturbation method and Fourier analysis. Closed analytical solutions are obtained for cylinders with arbitrary elastic modulus variations, revealing the relationships among buckling load, shell sizes, and elastic modulus functions. The presented solutions serve as benchmarks for buckling analyses of thin-walled cylinders with elastic modulus variations resulting from design, manufacturing processes, and material imperfections.