BELLOWS DESIGN EQUATIONS SUPPORTED BY LIMIT ANALYSIS

Abstract

ABSTRACT 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 twodimensional 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. LIMIT ANALYSIS Limit analysis is used to find the maximum load a structure made of ideally plastic material can carry. The deformations of an ideally plastic structure increase without bound at this load, which is termed the collapse load. The analysis can be performed using a closed form equation or finite element analysis (FEA). With FEA, a computer model of the structure is created with appropriate boundary conditions. The model is then exposed to stepwise loading. Component stresses are calculated at each load step. A yield criterion is selected which specifies the state of multiaxial stress corresponding to the onset of plastic flow. The yield criterion can be represented geometrically by a fixed limit surface in the principal stresses space. Commonly used limit surfaces are Tresca and von Mises. The stresses at every point in the structure must lie in or on the limit surface. Since limit analysis is normally based on a yield criterion, it is only applicable for materials operating at temperatures below the creep range