A Numerical Investigation on Stress Modal Analysis of Composite Laminated Thin Plates
Abstract
:1. Introduction
2. Theoretical Background
- Dynamic stress responses are straightforward related to material’s strength, e.g., in the criteria of vibration fatigue under random loadings [72]; and vibration fatigue failure of aircraft composite materials is frequently stress-induced high-cycle fatigue;
- Although the displacement fields of composite laminates are continuous, the stress distribution of each lamina may experience severe discontinuity due to the severe anisotropy. The SMSs can embody the orientation effect of each lamina, i.e., the same strain along different directions may result in different stresses because of the orthotropic properties;
- The strain modes measured at laminate’s surface in modal testing cannot reflect the internal stress state at a mode shape; while the internal SMSs can be easily captured in computational modal analysis, which will be useful for internal damage assessment for each layer.
- (a)
- The thickness distribution of the plate is uniform.
- (b)
- The material is linear elastic and 2-D orthotropic.
- (c)
- The damping is light, so that it can be neglected.
3. FEM Modelling
4. Results and Discussion
- (1)
- The stress mode distributions in different laminas will be different due to the orthotropic elastic properties. Because the maximum damage envelope of all layers is critically important in evaluating the strength of laminated plates (e.g., in the failure criteria of damage mechanics); therefore, herein, the envelope SMSs are considered.
- (2)
- The SMSs have different distributions with different stress components (e.g., for thin plates along the three important directions) and the invariants. For simplicity but without loss of generality, present study only considers the in-plane stresses, which are the most important stress components in damage criteria of composite laminates. For instance, the Tsai–Hill failure criterion can be written as , for the multi-axial random stress states (plane stress) in composite structures [78].
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
C | elastic matrix |
D | damping matrix |
f | exciting force vector |
j | imaginary unit |
K | stiffness matrix |
M | mass matrix |
H | displacement frequency response function |
Hσ | stress frequency response function |
S | compliance matrix |
x | nodal displacement vector |
w | out-of-plane deflection |
ϕ | displacement mode shape |
Φ | displacement modal matrix |
ϕσ | stress mode shape |
Φσ | stress modal matrix |
ω | modal frequency |
ε | strain vector |
σ | stress vector |
κ | modal curvature |
FEM | finite element method |
FRF | frequency response function |
SFRF | stress frequency response function |
SMA | stress modal analysis |
SMSs | stress mode shapes |
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Property/Notation | Value |
---|---|
Longitudinal modulus E11 (GPa) | 181 |
Transverse modulus E22 (GPa) | 10.3 |
Shear modulus G12 (GPa) | 7.17 |
Poisson’s ratio ν12 | 0.28 |
Mass density ρ (kg/m3) | 1600 |
Length a = b (mm) | 500 |
Thickness h (mm) | 1.2 |
Mode Number | Maximum Magnitude of the Stress Mode | |||||
---|---|---|---|---|---|---|
Initial Layup | Designed Layup | |||||
x | y | xy | x | y | xy | |
1 | 10.83 | 0.74 | 0.37 | 6.74 | 0.49 | 0.53 |
2 | 12.26 | 1.82 | 0.90 | 13.73 | 1.10 | 1.08 |
3 | 19.54 | 3.09 | 1.53 | 15.00 | 1.09 | 1.18 |
4 | 28.96 | 1.10 | 0.82 | 20.83 | 1.63 | 1.64 |
5 | 29.41 | 2.64 | 1.32 | 26.61 | 1.94 | 2.10 |
6 | 26.76 | 4.24 | 2.11 | 29.86 | 1.83 | 1.98 |
Mode Number | Modal Frequency (Hz) | ||
---|---|---|---|
Initial Layup | Designed Layup | Percent of Change (%) | |
1 | 54.4 | 52.9 | −2.7 |
2 | 80.2 | 101.4 | 26.5 |
3 | 123.8 | 111.2 | −10.2 |
4 | 135.6 | 161.2 | 18.9 |
5 | 160.1 | 183.5 | 14.6 |
6 | 179.0 | 191.5 | 7.0 |
7 | 208.4 | 235.1 | 12.8 |
8 | 239.6 | 259.6 | 8.4 |
9 | 258.2 | 289.5 | 12.1 |
10 | 280.1 | 295.6 | 5.5 |
11 | 284.0 | 322.8 | 13.7 |
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Zhou, Y.; Sun, Y.; Zeng, W. A Numerical Investigation on Stress Modal Analysis of Composite Laminated Thin Plates. Aerospace 2021, 8, 63. https://doi.org/10.3390/aerospace8030063
Zhou Y, Sun Y, Zeng W. A Numerical Investigation on Stress Modal Analysis of Composite Laminated Thin Plates. Aerospace. 2021; 8(3):63. https://doi.org/10.3390/aerospace8030063
Chicago/Turabian StyleZhou, Yadong, Youchao Sun, and Weili Zeng. 2021. "A Numerical Investigation on Stress Modal Analysis of Composite Laminated Thin Plates" Aerospace 8, no. 3: 63. https://doi.org/10.3390/aerospace8030063