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Three-dimensional strain rosettes: Pattern selection and performance evaluation

Reliability and precision of three-dimensional embedded strain-gage rosettes as affected by configuration are assessed theoretically. Some side effects of deadweight machine on model are pointed out by analysis of residuals

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Abstract

The configuration of three-dimensional strain rosettes is shown to be directly related to precision and reliability. Equations are given for computing these parameters, and several rosette configurations are compared accordingly.

Experimental techniques developed at Istituto di Metrologia “G. Colonnetti” are described. A case history is given, in which the analysis of deviations between expected and actual embedded rosette results throws some light on complex interactions between model and deadweight loading machine.

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Abbreviations

A :

product matrix (T′ T)

B :

inverse ofA matrix

b 0 :

constant term of the strain-vs.-load equation

b 1 :

first order term of the strain-vs.-load equation

b 2 :

second order term of the strain-vs.-load equation

C x :

number of singular configurations of three-dimensional rosettes with x grids failed

d :

least-squares estimate of strain tensor δ

e :

vector of strains\(\varepsilon _i\) measured by the grids of the rosette

g :

maximum number of grids lost in a rosette

k :

total number of grids of a rosette

L :

load

l i , m i , n i :

cosine directors of theith grid

P :

probability of rosette failure

p :

risk of single grid failure

R :

rosette reliability

T :

design matrix of the rosette

x :

number of grids failed

α:

angular position of loading point

δ:

strain tensor

ε, γ:

normal and shear strain components

\(\varepsilon _i\) :

strain along theith grid

η:

error (assumed to beN (0,\(\sigma ^2\))

\(\sigma ^2\) :

variance due to pure error

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Authors and Affiliations

  1. Politecnico di Torino, Torino, Italy

    S. Rossetto (Professor) & R. Levi (Professor)

  2. Istituto di Metrologia “Gustavo Colonnetti,”, Torino, Italy

    A. Bray (Director)

Authors
  1. S. Rossetto
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  2. A. Bray
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  3. R. Levi
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Rossetto, S., Bray, A. & Levi, R. Three-dimensional strain rosettes: Pattern selection and performance evaluation. Experimental Mechanics 15, 375–381 (1975). https://doi.org/10.1007/BF02319834

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