OICC Press Journal of Solid Mechanics 2008-7683 4 2 2012 06 30 An Analytical Solution for Inverse Determination of Residual Stress Field 114 127 EN S.A Faghidian Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University G.H Farrahi School of Mechanical Engineering, Sharif University of Technology D.J Smith Department of Mechanical Engineering, University of Bristol Journal Article 2012 06 30 An analytical solution is presented that reconstructs residual stress field from limited and incomplete data. The inverse problem of reconstructing residual stresses is solved using an appropriate form of the airy stress function. This function is chosen to satisfy the stress equilibrium equations together with the boundary conditions for a domain within a convex polygon. The analytical solution is demonstrated by developing a reference solution from which selected “measurement” points are used. An artificial error is then randomly added to “measurement” points for studying the stability of the reconstruction method utilizing Tikhonov-Morozov regularization technique. It is found that there is an excellent agreement between the model prediction and limited set of residual stress data in the sense of least-square approximation.