A mathematical method is derived which permits calculation, based upon linear shell theory, of all stresses and displacements in a precision welded bellows having any number of layers, when displaced due to internal fluid pressure. If the meridional shape contains large curvatures or sharp corners the shell theory is replaced by the theory of solid elastic tori, which is used also for including the effects of the welds. As computation errors would eventually invalidate solutions for bellows with too many layers, a boundary layer technique is devised to overcome this difficulty. The method may therefore be applied to a bellows with any large number of layers without increase in the overall percentage error in displacement. An exact error check is possible in the solution for the transverse shear, indicating with our present step-intervals and medium size computer, errors of less than one percent.

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