List of Figures
Fig. 2.1
Various hypotheses for plates and shells. . . . . . . . . . . . . . . . . . .
8
Fig. 3.1
Definition of base vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Fig. 4.1
The configurations of PbTiO 3 crystalline structure . . . . . . . . . . . 57
Fig. 4.2
The direct and converse effects of piezoelectric material. . . . . . . 57
Fig. 4.3
Orientation of reinforcement fibers . . . . . . . . . . . . . . . . . . . . . . . 62
Fig. 4.4
Schematic of different kinds of MFC models . . . . . . . . . . . . . . . 65
Fig. 4.5
Multi-layer composites with MFCs, reprinted from Ref. [18],
copyright 2015, with permission from ELSEVIER . . . . . . . . . . . 70
Fig. 5.1
Physical meaning of the resultant internal forces
and moments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Fig. 5.2
Degrees of freedom at any point on the mid-surface. . . . . . . . . . 80
Fig. 5.3
Rotation of the base vector triad by Euler angles u 1 and u 2 . . . 80
Fig. 5.4
Lagrange and Serendipity families of shell elements. . . . . . . . . . 83
Fig. 5.5
Element mapping between natural coordinates and curvilinear
coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Fig. 5.6
Schematic procedure for the Riks-Wempner method. . . . . . . . . . 97
Fig. 6.1
Asymmetric cross-ply laminated plate. . . . . . . . . . . . . . . . . . . . . 102
Fig. 6.2
Load-displacement curves of hinged cross-ply plate under a
uniform pressure: a small pressure, b large pressure, reprinted
from Ref. [5], copyright 2014, with permission from
ELSEVIER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
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 . . . . . . . . . . . . . . . . . . . 104
Fig. 6.4
Asymmetrically loaded hinged thin arch, reprinted from
Ref. [6], copyright 2014, with permission from ELSEVIER . . . . 105
Fig. 6.5
Static response of the asymmetrically loaded hinged thin arch,
reprinted from Ref. [6], copyright 2014, with permission
from ELSEVIER. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Fig. 6.6
Spherical shell under a pair of stretching and compressing
forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
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