Least-Squares Methods

  • Donald Berghaus
Chapter

Abstract

Least-squares is described as a method for solving problems where there is an excess of information available. This is often the case in experimental mechanics. The method can be used to include information from different sources; experimental and theoretical. The method is applied to curve fitting problems and to more general situations. Nonlinear least squares methods are described for fitting of approximation functions.

Keywords

Brittle Assure Doyle Illy Multiflash 

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References

  1. 1.
    Leland, O.M., Practical Least Squares, McGraw-Hill, New York, NY (1921)MATHGoogle Scholar
  2. 2.
    Sears, F. W., and Zemansky, M. W., College Physics, Part I, Mechanics, Heat, and Sound, Addison Wesley, Cambridge, MA (1952), p. 59Google Scholar
  3. 3.
    Dally, J.W., and Riley, W.F., “Experimental Stress Analysis”, McGraw-Hill, New York, NY (1978), Chapter 10Google Scholar
  4. 4.
    Hamming, R. W., Numerical Methods for Scientists and Engineers, McGraw-Hill, New York, NY (1962), p. 244–246MATHGoogle Scholar
  5. 5.
    Ibid, p. 361,362Google Scholar
  6. 6.
    Berghaus, D.G., Calculations for Experimental Stress Analysis Using the Personal Computer, Society for Experimental Mechanics., Bethel, CT, (1987), p. 34–36Google Scholar
  7. 7.
    Businger, P., and Golub, G.H., “Linear Least Squares Solutions Using Householder Transformations”, Numerische Mathematik, 7, (1965), p. 269–276MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Frocht, M.M., “Photoelasticity, 2”, John Wiley and Sons, New York, NY, (1948), p. 125–129Google Scholar
  9. 9.
    Berghaus, D.G., “Overdetermined Photoelastic Solutions Using Least- Squares”, Experimental Mechanics, 13, (1973), pp. 97–104CrossRefGoogle Scholar
  10. 10.
    Berghaus, D.G., and Aderholdt, R.E., “Photoelastic Analysis of Interlaminar Matrix Stresses in Fibrous Composite Models”, Experimental Mechanics, 15, (1975), p. 409–417CrossRefGoogle Scholar
  11. 11.
    Doyle, J.F., and Danyluk, H.T., “Integrated Photoelasticity for Axisymmetric Problems”, Experimental Mechanics, 18, (1978), p. 215–220CrossRefGoogle Scholar
  12. 12.
    Berghaus, D.G., “Combining Photoelasticity and Finite-element Methods for Stress Analysis Using Least-Squares, Experimental Mechanics, 31, (1991), p. 36–41CrossRefGoogle Scholar
  13. 13.
    Berghaus, D.G., “Adding the LaPlace Equation to Least Squares Photoelastic Stress Solutions”, Experimental Techniques, 13, (1989), p. 18–21CrossRefGoogle Scholar
  14. 14.
    Daniel, D., and Wood, F.S., Fitting Equations to Data, Wiley-Interscience, New York, NY (1971), Chapter 3MATHGoogle Scholar
  15. 15.
    Berghaus, D.G., “Fitting of Simple Approximation Functions Using Nonlinear Least Squares Methods”, Experimental Mechanics, 17, (1977), p. 14–20CrossRefGoogle Scholar
  16. 16.
    Woods, T.O., and Berghaus, D.G. “The Biaxial Loading Response of Powder Aluminum atElevated temperature”, Experrimental Mechanics, 34 (1994), p 249–255CrossRefGoogle Scholar
  17. 17.
    Woods, T.O., Berghaus, D.G., and Peacok, H.B., “Interparticle Movement and the Mechanical Behavior of Extruded Powder Aluminum at Elevated Temperature”, Experimental Mechannics, 38, (1998), p. 110–115CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Donald Berghaus
    • 1
  1. 1.Georgia Institute of TechnologyUSA

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