The buckling behavior of U-shaped bellows under pressure loads

Parametric design analysis of meridional deflection stresses in metal expansion bellows using gray relational grade

“…Thin-walled construction of the convolution makes the bellows particularly susceptible to overstressing and excessive deformation. Analytical derivation is based on the principle that when the internal pressurized fluid passes through a thin cylinder; initially, it bows at the center, due to which small initial bending angle is formed [19]. It is beneficial to determine the deflection stresses as there is an equivalent axial displacement of the convolution at root potion due to lateral load.…”

“…Figure 3 shows the bellows subjected to an initial bending angle (θ 0 ) due to internal pressurized fluid. Based on the criteria suggested for lateral loading due to internal pressure, by Tsukimori [19], the governing differential equation for the equivalent axial displacement is given as follows.…”

“…However, column squirm exists in large convolutions through compressive loads. EJMA provides limitations for these instabilities with the pressure-based stresses [18,19]. Merely, for instance, the pressure load can be predicted by aggregating real yield state strength and equation for maximum meridional bending stress [20].…”

“…According to Tsukimori et al [19], it is established that the bending angle (θ b ) is dependent on the strain at the root of the convolution and nearly equal to 2% of strain. The initial bending angle (θ 0 ) is considered as half of the θ b , as it is distributed at both ends of the bellows.…”

“…For the assessing of the in-plane instability, critical pressure ' P cr ' is given by, Jian et al [20] suggested the minimum internal pressure, measured to predict the critical pressure and instability due to in-plane squirm; the equation is given as, Based on Euler's column buckling theory, Tsukimori et al [19] developed the buckling critical pressure equation as follows:…”