Study on equivalent mechanical properties of U-shaped bellows based on novel implementation of asymptotic homogenization method

As typical metal thin-walled structure, bellows are used widely in various engineering fields, especially in storage and transportation of floating liquefied natural gas (FLNG) system on the sea. While the shapes of the bellows are relatively complex with the characteristics of geometric nonlinearity in the structure, it is quite challenging to calculate basic mechanical properties of the bellows accurately through theoretical analysis. Concurrently, both numerical simulation and experiments also require high computational and economic cost. Given the typical one-dimensional periodicity of the structure of U-shaped bellows, novel implementation of asymptotic homogenization (NIAH) method was secondary developed in finite element software and unit-cell model of the whole structure with periodic boundary conditions was established, realizing equivalent analysis of the overall mechanical properties of the bellows accurately and efficiently. By comparing the NIAH equivalent results with the fine finite element model results, it was found that the relative error was within 3.00 % and the calculation cost was reduced by 40 times. Compared with the experimental results, the error of NIAH equivalent results was also less than 6.00 %, which verified the accuracy and high efficiency of the NIAH equivalent method. Furthermore, the influence of unit-cell model with different structural sizes on the prediction accuracy of the NIAH equivalent stiffness results of the bellows was also discussed. This study provides a new effective method for the design and analysis of the structure of bellows.