Bellows Design Equations Supported by Limit Analysis

Limit analysis can be used to design metal bellows for pressure capacity. The objective of limit analysis is to prevent gross plastic deformation with an appropriate design margin. The primary advantage of limit analysis over other methods is that it can find the max. allowable limit load for the structure as a whole and not just for the individual parts. In the case of bellows, an allowable limit pressure can be found which assures a specified margin on plastic collapse. In this paper, a parametric FEA study is performed on a series of two-dimensional axisymmetric models of un-reinforced U-shaped bellows with wide ranging dimensions. The non-linear analysis gives the max. allowable limit pressure for each bellows based on limit analysis and a closed form equation is confirmed to accurately describe the FEA results. Combined with existing equations for column instability and external buckling, limiting design pressure equations are presented for bellows design.