Hole-drilling Eccentricity:钻Kong应变计法的偏心校正-开源
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Explanation of Matlab code
In this appendix the authors report guidelines of the correction method implemented in Matlab
®
programming language. Code consists of four subroutines called ecc_correction.m, step_j.m,
C.m and G.m. Rosette type is indicated in the name of the subroutines.
Next code can be used to start the correction method for type A rosettes:
[Ea_corrected,Eb_corrected,Ec_corrected]=ecc_correction_A(Eap,Ebp,Ecp,
ex,ey)
ecc_correction.m has five inputs. The first three are three column vectors with the twenty
strains measured in the gauges
a ,b
and
c
in
µm/m
. The fourth and the fifth are
e
x
and
e
y
in
µm
. This function calculates some values that are going to be used during the code (
e
b x
, e
b y
, e
cx
and
e
c y
), and loads the coefficients
δ
m pquv
stored in three matrices 6x21, 3x21 and 6x21 for m =
1, 2, 3, respectively.
ecc_correction.m calls the function step_j.m, which calculates the corrected strains for each step
j
following the flowchart represented in Fig. 6. Its inputs are the initial data of the flowchart and
the six stages are indicated as comments in the code.
In step_j.m is remarkable the way the angle
β
j
is calculated. An increment
∆ β
j
=0.001 º
has
been chosen for the iteration and the equality of the system (5) is achieved when:
100.01>¿
(
ε '
b
)
jj
|
β
j
(
ε '
b
)
jj
¿99.99
(B.1)
where the subscript
β
j
indicates
(
ε '
b
)
jj
calculated by iteration. These choices ensure a total
computation time of seconds.
Equations (7 – 8) have a discontinuity when the denominator is zero. Although in the practice is
very difficult to find this situation, it means that for some combinations of angles/eccentricities
near the discontinuity, equation (B.1) is only achieved when
∆ β
j
is very small, increasing
considerably the computation time. To avoid this,
β
j
is calculated by two independent ways:
considering equations 1 and 3 in system (5) and checking if the second equality is achieved, and
considering equations 1 and 2 and checking the third equation. In this way, when combination
of angles/eccentricities is near of the discontinuity, (B.1) is not achieved in one of the two ways
of calculation and
β
j
is taken from the second way.
step_j.m calls C.m, which calculates the values of
(
C
m
)
jk
and its arguments are
j , k
,
e
lx
and
e
l y
.
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