The Incremental Strain, Average Stress, Power Series, and Integral methods are examined as procedures for determining non-uniform residual stress fields using strain relaxation data from the hole drilling method. Some theoretical shortcomings in the Incremental Strain and Average Stress methods are described. It is shown that these two traditional methods are in fact approximations of the Integral Method. Theoretical estimates of the errors involved are presented for various stress fields. Also, some simple transformations of stress and strain variables are introduced so as to decouple the stress/strain equations and simplify the numerical solution.

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