Analysis of residual stresses in a long hollow cylinder

This paper presents an analytical method for solving the axisymmetric stress problem for a long hollow cylinder subjected to locally-distributed residual (incompatible) strains. This method is based on direct integration of the equilibrium and compatibility equations, which thereby have been reduced to the set of two governing equations for two key functions with corresponding boundary and integral conditions. The governing equations were solved by making use of the Fourier integral transformation. Application of the method is illustrated with an analysis of the welding residual stresses in a butt-welded thick-walled pipe.

► A solution to the axisymmetric stress problem for a hollow cylinder is constructed.
► The cylinder is subjected to a field of locally-distributed residual strains.
► The method is based on direct integration of the equilibrium equations.
► An application of our solution to analysis of welding residual stresses is considered.