Approximate calculation of residual welding stresses in cylindrical shells

Analysis of residual stresses in a long hollow cylinder

“…In such manner, we obtain two governing equations (12) and (19) for the key stresses s and s rz . These equations are the second order partial differential equations, which should be accompanied with four boundary conditions for the key stresses.…”

“…This condition is obtained by integration of Eq. (19) over the radial coordinate from k to r and comparison to Eq. (18).…”

“…A vast majority of the existing experiment-calculated methods employ numerical [11e18] or approximate [19,20] procedures. However, for efficient analysis of the residual stresses, as well as for solving inverse elasto-plastic problems (which necessarily occur when one applies certain experiment-calculated methods), exact analytical solutions are required.…”

“…One of the most efficient theoretical approaches to determination of the residual stresses is based on the method of conventional plastic strains [19,21]. According to this method, the material of a welded solid is assumed to be elastic at some distance from the axes of welded joints.…”