# Elastic local shell and stiffener-tripping buckling strength of ring-stiffened cylindrical shells under external pressure

### Significance

Ring-stiffened cylindrical shells, commonly used in offshore and submergible structures, are highly susceptible to buckling failures due to high external pressure. Four main buckling modes: overall, shell, tripping, and local exist and interact with each other. Since actual design does not permit overall bucking, overall-tripping and shell-tripping are the most common interactions considered in the designs. Conventional formulas have been developed to provide alternative means of calculating the buckling strength other than the complicated and costly finite element method. However, conventional formulas produce inaccurate results as they ignore some key parameters affecting buckling such as the influence of the cylindrical shape and stress on the web and the interaction between the cylindrical shell and ring-stiffeners.

To solve the inherent problems, Daisuke Shiomitsu (Ph.D. student) and Prof. Daisuke Yanagihara from Kyushu University, Department of Maritime Engineering, proposed two formulas for estimating the local shell and stiffener-tripping buckling strength of the ring-stiffened cylindrical shells under external pressure. The buckling strength estimated using these formulas were compared with those for finite element analysis and other conventional formulas to validate their appropriateness. Alternatively, the influence of the new considerations adopted in the new formulas was evaluated. Their work is published in the research journal, Thin-Walled Structures.

The first formula is based on the curved beam model and includes the effects of torsional stiffness and cylindrical shape. It can only estimate the tripping buckling strength. The second formula is based on the full shell model considering the interaction of the buckling deflection deformation between the cylindrical shell and ring stiffeners as well as the influence of the web stresses that are often ignored in other conventional formulas. This formula is derived based on the minimum potential energy principle and can estimate both the shell and tripping buckling strengths accurately.

Results showed that the first formula estimated smaller the tripping buckling than the conventional formulas. The smaller tripping buckling strength was attributed to the influence of the cylindrical shape and torsional stiffness effects. Additionally, an estimation error larger than that of the finite element analysis is also a clear indication that this formula is less accurate. Moreover, the second formula produced excellent results that agreed well with those of the finite element analysis. For instance, it was used to accurately estimate the strength of the tripping buckling mode of n = 0, which is nearly impossible with other conventional methods. The influence of stress, taken into account, largely contributed to the positive results. It was evident that the radial stress acting on the web before buckling is tension in the outside ring-stiffener and compression on the inside. Unlike the conventional formulas whose accuracy decrease with the decrease in the cylindrical shell thickness, the second proposed formula maintains the accuracy since it uses displacement functions with fixed conditions at the joining points between the cylindrical shell and the web.

In a nutshell, the study presented two formulas for estimating the local shell and stiffener-tripping buckling strength of ring-stiffened cylindrical shells under external pressure. The second formula produced accurate results than both the first and conventional formulas. In a Statement to Advances in Engineering, the authors noted that their study provides useful insights that will advance the future design of offshore and submergible structures.