104
6 Nonlinear Analysis of Piezoceramic Laminated Structures
Table 6.2 Mid-point displacements of cross-ply plate by LRT56 theory using SH85URI elements
Load (+q lb/in 2 )
Present (LRT56,
|w|/ h)
Reddy [2]
Basar et al. [3]
0.005
0.4303
0.429
0.429
0.01
0.8606
0.858
0.858
0.02
1.7208
1.71
1.717
0.03
2.5803
2.55
2.574
0.04
3.4385
3.37
3.430
0.05
4.2951
4.19
4.285
0.10
8.5413
7.92
8.525
0.25
20.5799
16.17
20.57
0.50
37.0014
24.82
37.03
0.75
48.8280
30.87
48.83
1.0
57.1631
35.69
57.14
2.0
73.7032
49.56
73.64
3.0
80.4214
59.65
80.36
4.0
84.0963
68.00
84.03
5.0
86.4767
75.33
86.41
Fig. 6.3 Load-displacement
curves of simply supported
cross-ply plate under a
uniform pressure, reprinted
from Ref. [5], copyright
2014, with permission from
ELSEVIER
0
20
40
60
80
100
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
Transverse deflection (|w|/h)
Load (lb/in
2
)
+q, LRT56 (SH851URI)
+q, LRT56 (SH851FI)
+q, LRT5 (SH851URI)
+q, MRT5 (SH851URI)
+q, RVK5 (SH851FI)
+q, Reddy (1989)
+q, Basar (1993)
+q, Kreja (2006)
+q, ANSYS (SHELL281)
+q, Linear (SH851URI)
by increasing the number of elements. It can be seen from the figure that results
obtained by the model of RVK5 with SH851FI agree very well with those reported
by Reddy [2], who implemented the same type of nonlinear theory in the model but
based on the TOSD hypothesis. In addition, the results indicate that the commercial
software ANSYS predicts similar to the MRT5 and LRT5 models in this example.
6 Nonlinear Analysis of Piezoceramic Laminated Structures
Table 6.2 Mid-point displacements of cross-ply plate by LRT56 theory using SH85URI elements
Load (+q lb/in 2 )
Present (LRT56,
|w|/ h)
Reddy [2]
Basar et al. [3]
0.005
0.4303
0.429
0.429
0.01
0.8606
0.858
0.858
0.02
1.7208
1.71
1.717
0.03
2.5803
2.55
2.574
0.04
3.4385
3.37
3.430
0.05
4.2951
4.19
4.285
0.10
8.5413
7.92
8.525
0.25
20.5799
16.17
20.57
0.50
37.0014
24.82
37.03
0.75
48.8280
30.87
48.83
1.0
57.1631
35.69
57.14
2.0
73.7032
49.56
73.64
3.0
80.4214
59.65
80.36
4.0
84.0963
68.00
84.03
5.0
86.4767
75.33
86.41
Fig. 6.3 Load-displacement
curves of simply supported
cross-ply plate under a
uniform pressure, reprinted
from Ref. [5], copyright
2014, with permission from
ELSEVIER
0
20
40
60
80
100
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
Transverse deflection (|w|/h)
Load (lb/in
2
)
+q, LRT56 (SH851URI)
+q, LRT56 (SH851FI)
+q, LRT5 (SH851URI)
+q, MRT5 (SH851URI)
+q, RVK5 (SH851FI)
+q, Reddy (1989)
+q, Basar (1993)
+q, Kreja (2006)
+q, ANSYS (SHELL281)
+q, Linear (SH851URI)
by increasing the number of elements. It can be seen from the figure that results
obtained by the model of RVK5 with SH851FI agree very well with those reported
by Reddy [2], who implemented the same type of nonlinear theory in the model but
based on the TOSD hypothesis. In addition, the results indicate that the commercial
software ANSYS predicts similar to the MRT5 and LRT5 models in this example.