Numerical Method for Calculating Stresses in Bellows
In this numerical approach, it is assumed that all convolutions of a bellows operate under identical conditions; consequently, the analysis focuses on a single half-wave of the bellows. As a result, the end convolutions-which are subject to different boundary conditions than the intermediate ones-are excluded from the analysis. The numerical method is based on the nonlinear equations formulated by E. Reissner for the axisymmetric deformation of thin-walled shells of revolution with variable wall thickness. The derivation of the Reissner equations relies on standard assumptions from thin-shell theory, including the premises that the shell thickness is small relative to the principal radii of curvature, and that the material is both homogeneous and isotropic. However, these assumptions can introduce certain errors into the calculations, as the manufacturing processes-such as the rolling and drawing of the tube blank, followed by the plastic forming of the convolutions-often induce anisotropy and non-homogeneity in the mechanical properties of the material.