144
7 Numerical Analysis of Macro-fiber Composite Structures
ε11 (MPa)
0
100
200
300
0
50
−1
0
1
ε13 (MPa)
0
100
200
300
0
50
−1
0
1
(a) MFC-d33 with fiber angle of 0
◦
ε11 (MPa)
0
100
200
300
0
50
−1
0
1
ε13 (MPa)
0
100
200
300
0
50
−1
0
1
(b) MFC-d33 with fiber angle of 30
◦
ε11 (MPa)
0
100
200
300
0
50
−0.5
0
0.5
ε13 (MPa)
0
100
200
300
0
50
−0.5
0
0.5
(c) MFC-d33 with fiber angle of 45
◦
ε11 (MPa)
0
100
200
300
0
50
−1
0
1
ε13 (MPa)
0
100
200
300
0
50
−1
0
1
(d) MFC-d33 with fiber angle of 60
◦
ε11 (MPa)
0
100
200
300
0
50
−1
0
1
ε13 (MPa)
0
100
200
300
0
50
−1
0
1
(e) MFC-d33 with fiber angle of 75
◦
ε11 (MPa)
0
100
200
300
0
50
−1
0
1
ε13 (MPa)
0
100
200
300
0
50
−1
0
1
(f) MFC-d33 with fiber angle of 90
◦
Fig. 7.7 Stress (ε 11 ,ε 13 ) distribution of the aluminum plate with MFC-d33 patches having different
fiber angles, reprinted from Ref. [4], copyright 2015, with permission from ELSEVIER
7.2 Nonlinear Analysis of MFC Structures
7.2.1 Cantilevered Plate Bonded with Multi-MFC Patches
In this section, geometrically nonlinear analysis are performed on multi-MFC
bonded structures. First, a clamped plate integrated with multi-patches of MFCd33 is studied, as shown in Fig. 7.10. The host plate structure is made of T300/976
graphite/epoxy angle-ply laminates, with the stacking sequence of [−45
◦
/45
◦ ] from
the lower to the upper positions. The dimensions of the plate and MFC-d33 patches
are respectively 284 × 44 × 0.2 mm
3 and 56 × 28 × 0.3 mm
3 . The thickness for
each substrate layer of composites is 0.1 mm. The distribution spacing of MFC
patches on the plate is d = 12 mm. The material properties are give in Table 7.1.
Four different discretization schemes are investigated in order to study the convergence performance, namely 9 × 3, 13 × 3, 13 × 4 and 17 × 4, as shown in Fig. 7.11.
In the simulation, eight-node quadrilateral elements with five mechanical DOFs
at each node and one electric DOF on each element are considered using uniformly reduced integration scheme. An equal driving electric voltage of 800 V
7 Numerical Analysis of Macro-fiber Composite Structures
ε11 (MPa)
0
100
200
300
0
50
−1
0
1
ε13 (MPa)
0
100
200
300
0
50
−1
0
1
(a) MFC-d33 with fiber angle of 0
◦
ε11 (MPa)
0
100
200
300
0
50
−1
0
1
ε13 (MPa)
0
100
200
300
0
50
−1
0
1
(b) MFC-d33 with fiber angle of 30
◦
ε11 (MPa)
0
100
200
300
0
50
−0.5
0
0.5
ε13 (MPa)
0
100
200
300
0
50
−0.5
0
0.5
(c) MFC-d33 with fiber angle of 45
◦
ε11 (MPa)
0
100
200
300
0
50
−1
0
1
ε13 (MPa)
0
100
200
300
0
50
−1
0
1
(d) MFC-d33 with fiber angle of 60
◦
ε11 (MPa)
0
100
200
300
0
50
−1
0
1
ε13 (MPa)
0
100
200
300
0
50
−1
0
1
(e) MFC-d33 with fiber angle of 75
◦
ε11 (MPa)
0
100
200
300
0
50
−1
0
1
ε13 (MPa)
0
100
200
300
0
50
−1
0
1
(f) MFC-d33 with fiber angle of 90
◦
Fig. 7.7 Stress (ε 11 ,ε 13 ) distribution of the aluminum plate with MFC-d33 patches having different
fiber angles, reprinted from Ref. [4], copyright 2015, with permission from ELSEVIER
7.2 Nonlinear Analysis of MFC Structures
7.2.1 Cantilevered Plate Bonded with Multi-MFC Patches
In this section, geometrically nonlinear analysis are performed on multi-MFC
bonded structures. First, a clamped plate integrated with multi-patches of MFCd33 is studied, as shown in Fig. 7.10. The host plate structure is made of T300/976
graphite/epoxy angle-ply laminates, with the stacking sequence of [−45
◦
/45
◦ ] from
the lower to the upper positions. The dimensions of the plate and MFC-d33 patches
are respectively 284 × 44 × 0.2 mm
3 and 56 × 28 × 0.3 mm
3 . The thickness for
each substrate layer of composites is 0.1 mm. The distribution spacing of MFC
patches on the plate is d = 12 mm. The material properties are give in Table 7.1.
Four different discretization schemes are investigated in order to study the convergence performance, namely 9 × 3, 13 × 3, 13 × 4 and 17 × 4, as shown in Fig. 7.11.
In the simulation, eight-node quadrilateral elements with five mechanical DOFs
at each node and one electric DOF on each element are considered using uniformly reduced integration scheme. An equal driving electric voltage of 800 V