An Analytical Solution for Inverse Determination of Residual Stress Field

Subject Areas : Engineering

S.A Faghidian ¹ (Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University)
G.H Farrahi ² (School of Mechanical Engineering, Sharif University of Technology)
D.J Smith ³ (Department of Mechanical Engineering, University of Bristol)

Received: 2012-01-26 Accepted : 2012-04-01 Published : 2012-06-30

Keywords:

References:

[1] Smith D.J., Farrahi G.H., Zhu W X., McMahon C.A., 2001, Obtaining multiaxial residual stress distributions from limited measurements, Materials Science and Engineering A 303: 281–291.

[2] Hill M.R., 1996, Determination of residual stress based on the estimation of eigenstrain, Ph.D. Thesis. Stanford University.

[3] Cao Y.P., Hu N., Lu J., Yao Z.H., 2002, An inverse approach for constructing residual stress field induced by welding, Journal of Strain Analysis for Engineering Design 37: 345–359.

[4] Qian X., Yao Z., Cao Y., Lu J., 2005, An inverse approach to construct residual stresses existing in axisymmetric structures using BEM, Journal of Engineering Analysis with Boundary Elements 29: 986–99.

[5] Korsunsky A.M., Regino G.M., Nowell D., 2007, Variational eigenstrain analysis of residual stresses in a welded plate, International Journal of Solids and Structures 44(13): 4574–4591.

[6] Jun T.S., Korsunsky A.M., 2010, Evaluation of residual stresses and strains using the eigenstrain reconstruction method, International Journal of Solids and Structures 47:1678–1686.

[7] Ballard P., Constantinescu A., 1994, On the inversion of subsurface residual stresses from surface stress measurements, Journal of the Mechanics and Physics of Solids 42(11): 1767-1787.

[8] Schajer G.S., Prime M.B., 2006, Use of inverse solutions for residual stress measurements, Journal of Engineering Materials and Technology 128: 375-382.

[9] Hoger A., 1986, On the determination of residual stress in an elastic body, Journal of Elasticity 16: 303-324.

[10] Mura T., Gao Z., 1991, Inverse method in micromechanics of defects in solids, Proceedings of the 3rd International Conference on Residual Stress 1157-1167.

[11] Robertson R.L., 1998, Determining residual stress from boundary measurements: a linearized approach, Journal of Elasticity 52: 63–73.

[12] Moore M.G., Evans W.P., 1958, Mathematical correction for stress in removed layers in X-ray diffraction residual stress analysis, S A E Transactions 66: 340-345.

[13] Faghidian S.A., 2010, Estimation of Residual Stress Field Using Limited Measurements, Ph.D. Thesis. Sharif University of Technology, Tehran, Iran.

[14] Farrahi G.H., Faghidian S.A., Smith D.J., 2009, An inverse approach to determination of residual stresses induced by shot peening, International Journal of Mechanical Science 51: 726–731.

[15] Farrahi G.H., Faghidian S.A., Smith D.J., 2009, Reconstruction of residual stresses in autofrettaged thick-walled tubes from limited measurements, International Journal of Pressure Vessel and Piping 86: 777-784.

[16] Farrahi G.H., Faghidian S.A., Smith D.J., 2009, A new analytical approach to reconstruct residual atresses due to turning Process, Proceeding of World Academy of Science Engineering and Technology 55: 453-457.

[17] Farrahi G.H., Faghidian S.A., Smith D.J., 2010, An inverse method for reconstruction of the residual stress field in welded plates, Journal of Pressure Vessel Technology - Transactions of the ASME 132: 061205-1:9.

[18] Faghidian S.A., Goudar D., Farrahi G.H., Smith D.J., 2011, Measurement analysis and reconstruction of residual stresses, Journal of Strain Analysis for Engineering Design 47(4): 254-264.

[19] Gurtin M.E., 1972, The Linear Theory of Elasticity, Handbuch der Physik, Vol. VIa/2. Springer-Verlag, Berlin.

[20] Cheney E.W., 1982, Introduction to Approximation Theory,American Mathematical Society, Chelsea Publishing, New York.

[21] Groetsch C.W., 2007, Stable Approximate Evaluation of Unbounded Operators, Springer, Berlin.

[22] Kandil F.A., Lord J.D., Fry A.T., Grant P.V., 2001, A Review of Residual Stress Measurement Methods a Guide to Technique Selection, MATC (A) 04, UK National Physical Laboratory (NPL) Materials Centre report .

[23] King A.C., Billingham J., Otto S.R., 2003, Differential Equations: Linear, Nonlinear, Ordinary, Partial. Cambridge University Press, Cambridge.

[24] Hirota R.Y., 2004,The Direct Method in Soliton Theory, Cambridge University Press, Cambridge.

[25] Demmel J.W., 1997, Applied Numerical Linear Algebra, SIAM (Society for Industrial and Applied Mathematics), Philadelphia.