Appendix C
Normalization
C.1 Physical Components of the Strains
The relations between the original and normalized components of the Green strain
tensor in the three defined curvilinear coordinate systems are shown in Table C.1,
with the general coefficients in Table C.2.
Table C.1 Physical quantities of the Green strains
Sphere
Cylinder
Plate
General
ˆ
n
ε 11
R 2
(R + Θ 3 ) 2
n
ε 11
n
ε 11
s 2
1
n
ε 11
ˆ
n
ε 22
1
(R + Θ 3 ) 2 sin 2
Θ 1
R
n
ε 22
1
(R + Θ 3 ) 2
n
ε 22
n
ε 22
s 2
2
n
ε 22
ˆ
n
ε 12
R
(R + Θ 3 ) 2 sin
Θ 1
R
n
ε 12
1
(R + Θ 3 )
n
ε 12
n
ε 12
s 1 s 2
n
ε 12
ˆ
n
ε 13
R
R + Θ 3
n
ε 13
n
ε 13
s 1
n
ε 13
ˆ
n
ε 23
1
(R + Θ 3 ) sin
Θ 1
R
n
ε 23
1
(R + Θ 3 )
n
ε 23
n
ε 23
s 2
n
ε 23
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2021
S.-Q. Zhang, Nonlinear Analysis of Thin-Walled Smart Structures, Springer Tracts
in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9857-9
173