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Application of the least-squares method to photoelastic analysis

Two global methods for determining certain key parameters from full-field fringe patterns based on the method of least squares are presented

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Abstract

In this paper, the linear and nonlinear leastsquares methods are developed in matrix notation as solution schemes to determine key parameters from whole-field fringe patterns. Examples of the proposed methods to the determination of the photoelastic-fringe constant from a disk in diametral compression and the opening-mode geometric stress-intensity factor from the photoelastic-fringe loops in the neighborhood of a crack tip are presented. In the latter example, the location of the crack tip is treated as an unknown to be determined from the analysis.

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Abbreviations

r, θ:

polar coordinates

x, y :

Cartesian coordinates

R :

radius of circular disk

N :

photoelastic-fringe oder

f o :

photoelastic-fringe constant

t :

model thickness

A, B, C :

constants

P :

magnitude of a point load

K 1 :

opening-mode stress-intensity factor

σ 0x :

nonsingular, far-field stress

a :

crack length

W :

plate width

x 0 , y 0 :

location of crack tip

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Authors and Affiliations

  1. Structural Reliability Section, Marine Technology Division, Naval Research Laboratory, 20375, Washington, DC

    Robert J. Sanford (Head)

Authors
  1. Robert J. Sanford
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Sanford, R.J. Application of the least-squares method to photoelastic analysis. Experimental Mechanics 20, 192–197 (1980). https://doi.org/10.1007/BF02327598

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  • DOI: https://doi.org/10.1007/BF02327598

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