The prestresses in the walls of multilayered weld-wrapped cylindrical pressure vessels are mainly created by the transverse shrinkage of the welded layers. Current design practices consider only the shrinkage of longitudinal weld seams, resulting from constant temperature gradients. Such practices ignore the contribution to shrinkage from the remaining part of the welded plate and would, therefore, yield approximate values for the corresponding prestresses. In the present work the shrinkage of the full layer is determined, and hence a more accurate method for predicting the weld wrapping stresses is offered. The heat transfer problem during welding is addressed and modeled. A three-dimensional heat conduction problem with a heat source traveling at constant speed is formulated and solved. Using Green’s function, the transient temperature distribution is determined. A two-dimensional model is also employed, and the corresponding temperature solution is obtained. A numerical example for the two-dimensional model is worked out for a single welded layer. Comparison between the value of the layer shrinkage calculated by the method described in this paper (variable layer temperature) and that obtained by the current industry method (constant temperature gradient) shows that the latter yields a higher (more conservative) value, and hence will underpredict the prestresses in the layer and the vessel.

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