Theoretical and Numerical Study of the Buckling of Axially Compressed Bimodular Thin Cylindrical Shells

Bimodular materials refer to materials that exhibit distinct elastic properties under tensile and compressive loading conditions. This study aims to analyze the buckling problem of bimodular thin cylindrical shells under axial compressive loading. In existing studies on the buckling behavior of thin shells, the bimodular effect of materials is rarely considered due to the complexity of the analysis. Therefore, based on the elasticity theory of different moduli, this paper presents a theoretical and numerical study on the buckling problem of thin cylindrical shells with bimodular effect under axial compression. Based on the deformation characteristics of thin cylindrical shells under axial compression before and after buckling, a simplified mechanical model suitable for the buckling analysis of bimodular axially compressed thin cylindrical shells is established. The simplified mechanical model proposed in this paper decouples the membrane effect and bending effect during shell buckling by introducing the concept of the physical neutral layer. It divides the shell cross-section into tensile and compressive regions according to the bending effect component, thereby fully accounting for the influence of the bimodular effect of materials on the lateral bending stiffness of the shell. Subsequently, through this simplified mechanical model, the analytical expression for the linear critical load of bimodular thin cylindrical shells under axial compression is obtained. Eigen Value buckling analysis of bimodular axially compressed thin cylindrical shells based on ABAQUS is carried out to validate the correctness of the analytical solution. The results indicate that the shell height L, the radius-to-thickness ratio R/t, and the tension-to-compression modulus ratio E⁺/E^- have significant influences on their linear critical load. Moreover, the larger the tensile to compressive modulus ratio, the more sensitive the linear critical load of the shell is to the bimodular effect of materials. Specifically, when the E⁺/E^- ratio of the shell equals 1/2, the corresponding linear critical load is approximately 10% higher than that predicted by the classical solution. Meanwhile, when the E⁺/E^- ratio equals 2, the linear critical load of the shell is approximately 21% lower than that predicted by the classical solution. The novelty of this study lies in that, for the first time, based on the simplified mechanical model of tension-compression subarea, the influence of bimodular effect of materials is considered in the buckling analysis of thin cylindrical shells under axial compression, which provides a new analytical idea for the refined analysis and optimal design on it.