Chapter 7
Numerical Analysis of Macro-fiber
Composite Structures
Abstract This chapter deals with the simulation of MFC bonded structures using
the numerical models developed in previous chapters. First the model is validated
by MFC bonded plate structure, in which two typical types of MFCs are considered,
MFC-d31 and MFC-d33. Then, various geometrically nonlinear models are applied
to compute multi-MFC integrated pate and cylindrical shell structures. In both linear and nonlinear analysis, various piezo-fiber orientation angles are considered, to
demonstrate the influences on structural response.
7.1 Linear Analysis of MFC Structures
7.1.1 Validation Test
The first validation test is conducted on a cantilevered plate bonded with MFC-d33
patches on the top and bottom surfaces, which was proposed by Bowen et al. [1],
as shown in Fig. 7.1. The host structure is an aluminum plate, with the material
properties of the Young’s modulus Y = 70 GPa and the Possion’s ratio ν = 0.32.
The dimensions of the MFC plate are 300 × 75 × 1.97 mm
3 , while those of MFCd33 patches are 85 × 57 × 0.3 mm
3 (M8557-P1, Smart Material Corp. [2]). The
MFC patches are bonded at a distance d = 15 mm away from the clamped edge, see
Fig. 7.1. The material parameters of MFC-d33 are given in Table 7.1, based on the
studies of Williams et al. [3] and Bowen et al. [1], which are slightly different from
those provided by Smart Material Corp. [2].
A constant voltage loading of 400 V (electric field 400/0.5 V/mm) is applied on
the top MFC-d33 patch. The vertical displacements of the central line are calculated
and presented in Fig. 7.2, with the corresponding date listed in Table 7.2. With the
comparison of the current results and those obtained by ANSYS and experimental
investigations in Bowen et al. [1], a good agreement has been reached. Thus, the
present FE model is verified to be accurate enough for the simulation of MFC actuated
structures (Fig. 7.2 and Table 7.2).
© 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_7
137
Numerical Analysis of Macro-fiber
Composite Structures
Abstract This chapter deals with the simulation of MFC bonded structures using
the numerical models developed in previous chapters. First the model is validated
by MFC bonded plate structure, in which two typical types of MFCs are considered,
MFC-d31 and MFC-d33. Then, various geometrically nonlinear models are applied
to compute multi-MFC integrated pate and cylindrical shell structures. In both linear and nonlinear analysis, various piezo-fiber orientation angles are considered, to
demonstrate the influences on structural response.
7.1 Linear Analysis of MFC Structures
7.1.1 Validation Test
The first validation test is conducted on a cantilevered plate bonded with MFC-d33
patches on the top and bottom surfaces, which was proposed by Bowen et al. [1],
as shown in Fig. 7.1. The host structure is an aluminum plate, with the material
properties of the Young’s modulus Y = 70 GPa and the Possion’s ratio ν = 0.32.
The dimensions of the MFC plate are 300 × 75 × 1.97 mm
3 , while those of MFCd33 patches are 85 × 57 × 0.3 mm
3 (M8557-P1, Smart Material Corp. [2]). The
MFC patches are bonded at a distance d = 15 mm away from the clamped edge, see
Fig. 7.1. The material parameters of MFC-d33 are given in Table 7.1, based on the
studies of Williams et al. [3] and Bowen et al. [1], which are slightly different from
those provided by Smart Material Corp. [2].
A constant voltage loading of 400 V (electric field 400/0.5 V/mm) is applied on
the top MFC-d33 patch. The vertical displacements of the central line are calculated
and presented in Fig. 7.2, with the corresponding date listed in Table 7.2. With the
comparison of the current results and those obtained by ANSYS and experimental
investigations in Bowen et al. [1], a good agreement has been reached. Thus, the
present FE model is verified to be accurate enough for the simulation of MFC actuated
structures (Fig. 7.2 and Table 7.2).
© 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_7
137