The buckling of spherical-cylindrical composite shells by external pressure


Shell structures have increasingly attracted attention for a range of potential engineering applications. For instance, vibration, dynamic and buckling analysis are necessary for the perfect application of shell structures in soft biological, hyperelasticity, and composite material systems. Among the available shell structures, spherical-cylindrical composite shells are among the commonly used materials in ocean engineering. Like pressurized shell structures, it is highly recommendable to analyze the buckling behaviors of spherical-cylindrical shells to overcome the potential negative effects of external pressures generated with an increase in the depth of the water. This is considered critical in enhancing the design reliability and functionality of the composite shells because it is a key indicator for evaluating their structural performance. Notably, composite sandwich structures comprising core layers and two skins are known for their numerous advantages, including improved heat insulation, high specific stiffness and strength, and large critical buckling load than the most commonly used single-layer structures.

The vibration behaviors of ordinally cylindrical shells have been extensively studied in the literature using mostly the force method based on various assumptions. The force method involves separating the cylindrical and spherical parts and determining their moment solutions separately. Moreover, the original structure can be restored if the moments and boundary forces of the components satisfy the underlying deformation conditions. Unfortunately, the buckling analysis of these structures remains largely underexplored despite its practical implications. Despite using some methods used in the vibration analysis, they have several limitations that hinder their practical applications. Thus, developing more effective strategies of accurate buckling analysis of spherical-cylindrical shells is highly desirable.

On this account, Dr. Junpeng Liu, Mr. Bo Yu and Professor Menglan Duan from the China University of Petroleum in collaboration with Dr. Yang Zhou from Shanghai University and Dr. Yi Zhang Chinese Academy of Geological Sciences, proposed a new approximate analytical approach to investigate the buckling of spherical-cylindrical composite shells subjected to uniform external pressures. The composite shells were comprised of a single layer spherical part and metal honeycomb core-based cylindrical part. The lower and upper metal panels were connected to the honeycomb core layer via an adhesive. The critical buckling pressure was determined via a generalized Galerkin method considering the effects of the transverse shear strain. Finally, the obtained results were compared to the finite element model to validate the feasibility of the analytical solution. The work is currently published in the journal, Composite Structures.

Results showed that the effect of the hemispherical shell on the cylindrical shell was the same as the elastic support with stiffness. Thus, the problem was transformed into analyzing the buckling of sandwich cylindrical shells with fixed elastic support. The derived analytical formulas allowed for accurate calculation of the critical buckling pressures with shell structure ratios exceeding or equal to 2. Furthermore, the formulas were also applicable to the spherical-cylindrical composite sandwich shell with other material properties. It was worth noting that the theoretical results were in good agreement with the experimental results, indicating the feasibility of the theoretical approach.

In summary, the authors proposed a new approximate analytical solution to analyze the buckling behavior of the spherical-cylindrical composite shells subjected to uniform external pressure. The results confirmed the applicability of the proposed solution for accurate buckling analysis. In a statement to Advances in Engineering, first author, Dr. Junpeng Liu said the study lay the foundation for analyzing the buckling behaviors of spherical-cylindrical composite shell structures used in various engineering applications.


Liu, J., Yu, B., Zhou, Y., Zhang, Y., & Duan, M. (2021). The buckling of spherical-cylindrical composite shells by external pressureComposite Structures, 265, 113773.

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