In estimation of residual stresses, the existing methods are mainly based on the idea that variation of strains on the surface of the object is measured by sectioning continuously until there is no variation of the measured strains, which corresponds to the residual stresses. In this kind of method, some definite mathematical relation between the variation of stresses and the released surface force is required. This kind of relation was obtained for the cases where the geometry, boundary condition, and pattern of residual stress distribution are simple. This difficulty is solved when numerical analytical methods, such as the finite element method, etc. are applied.
In this paper, a general theory is developed based on the finite element method. With this method, three dimensional residual stresses can be measured. Furthermore, reliability of estimated values, of residual stresses by this method is mathematically studied when error is contained in the measured strains.