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Experimental Mechanics

, Volume 4, Issue 2, pp 37–47 | Cite as

Various forms of the strain-displacement relations applied to experimental strain analysis

Strain-displacement relations are presented in a general way and modified forms are developed for three special cases
  • V. J. Parks
  • A. J. Durelli
Article

Abstract

The purpose of this paper is to present the strain-displacement relations in a general way and to develop modified forms for three special cases which have application in experimental strain analysis:
  1. 1.

    Small rotations—large strains

     
  2. 2.

    Small strains—large rotations

     
  3. 3.

    Small strains—small rotations

     

The development will be made for two definitions of strain: (a) ratio of change of length to initial length (Lagrangian description), and (b) ratio of change of length to final length (Eulerian description).

An example of the error introduced when each of the modified expressions is used is analyzed and graphically represented. Applications to several experimental strain-analysis methods are reviewed. The general relation and each of the modified forms are illustrated with the moiré pattern of a uniform strain field subjected to the conditions of the three special cases.

Keywords

Mechanical Engineer General Relation Fluid Dynamics Modify Form Strain Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Love, A. E. H., “A Treatise on the Mathematical Theory of Elasticity,”4th ed., Dover Publications, New York, p.37, 1944.Google Scholar
  2. 2.
    Sokolnikoff, I. S., “Mathematical Theory of Elasticity,”2d Ed., McGraw-Hill Book Co., Inc., New York, p.6, 1956.Google Scholar
  3. 3.
    Timoshenko, S. andGoodier, J. N., “Theory of Elasticity,”2d Ed., McGraw-Hill Book Co., Inc., New York, p.5, 1951.Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1964

Authors and Affiliations

  • V. J. Parks
    • 1
  • A. J. Durelli
    • 1
  1. 1.Department of Civil EngineeringThe Catholic University of AmericaWashington, D. C.

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