Analytic solution of the residual stress in the axial symmetry retaining ring

The analytical solution can illuminate the mechanics views comprehensively, and also can promote the generation of the numerical solution as a standard solution. Therefore it has great values in the study of theory and the engineering field. This paper focus on studying the analytical solution by combining the mathematics with elasticity. On the basis of studying analytical solution of the residual stress in the axial symmetry object, we will mainly discuss the residual stress of axial symmetry anamorphic retaining ring, then educes analytical solution through constructing displacement function. At last, on the basis of this conclusion, we will analyze the instance that the inflexion of the retaining ring moves outside, in which, the theory of the axial symmetry column thin shell will be adopted, and we will also construct a new displacement function to work out the analytical solution of the residual stress under this instance.