Appendix B
Strain Fields of LRT56 Theory
The Green-Lagrange strain terms (
n
ε αβ ,
n
ε α3 and
0
ε 33 = 0) can be derived as
0
ε 11 =
0
v 1,1 − b 1
0
v 3 (LIN5)
+
1
2
a 1 (
0
v 1,1 )
2 + a 1 (b 1 )
2 (
0
v 3 )
2 + a 2 (
0
v 2,1 )
2 + a 2 (t 1 )
2 (
0
v 2 )
2 + (
0
v 3,1 )
2 + (c 1 )
2 (
0
v 1 )
2
+
1
2
−a 1 b 1
0
v 1,1
0
v 3 − a 1 b 1
0
v 3
0
v 1,1 + a 2 t 1
0
v 2,1
0
v 2 + a 2 t 1
0
v 2
0
v 2,1 + c 1
0
v 3,1
0
v 1 + c 1
0
v 1
0
v 3,1
(B.1)
0
ε 22 =
0
v 2,2 + t 2
0
v 1 − b 2
0
v 3 (LIN5)
+
1
2
a 1 (
0
v 1,2 )
2
+
a 1 (t 1 )
2
+ (c 2 )
2
(
0
v 2 )
2
+ a 2 (
0
v 2,2 )
2
+ a 2 (t 2 )
2
(
0
v 1 )
2
+a 2 (b 2 )
2
(
0
v 3 )
2
+ (
0
v 3,2 )
2
+
1
2
a 1 t 1
0
v 1,2
0
v 2 + a 1 t 1
0
v 2
0
v 1,2 + a 2 t 2
0
v 2,2
0
v 1 + a 2 t 2
0
v 1
0
v 2,2
+
1
2
−a 2 b 2
0
v 2,2
0
v 3 − a 2 b 2
0
v 3
0
v 2,2 + c 2
0
v 3,2
0
v 2 + c 2
0
v 2
0
v 3,2
+
1
2
−a 2 t 2 b 2
0
v 1
0
v 3 − a 2 t 2 b 2
0
v 3
0
v 1
(B.2)
© 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
167