Analysis of the Effect of an Open Hole on the Buckling of a Compressed Composite Plate
Abstract
:1. Introduction
2. The Subject of Study
3. Methodology
4. Experimental Study
- a1, a2—unknown parameters of the function,
- P—load,
- Pcr—critical load,
- u—shortening of the plate corresponding to the critical load.
5. FEM Analysis
- [K]—structural stiffness matrix,
- [H]—stress stiffness matrix,
- λi—i-th eigenvalue,
- ψ—i-th eigenvector of displacement.
6. Discussion of the Results
- δ—relative error,
- FEM—numerical results,
- EXP—experimental values.
S_Ø0 mm | S_Ø2 mm | S_Ø4 mm | S_Ø8 mm | |||
---|---|---|---|---|---|---|
S1 [45|−45|90|0]s | FEM | [N] | 199 | 198 | 194 | 179 |
EXP | [N] | 187 | 182 | 178 | 163 | |
relative error | [%] | 6.03% | 8.08% | 8.25% | 8.94% | |
S2 [0|−45|45|90]s | FEM | [N] | 649 | 644 | 628 | 573 |
EXP | [N] | 610 | 585 | 572 | 524 | |
relative error | [%] | 6.01% | 9.02% | 8.92% | 8.55% | |
S3 [0|90|0|90]s | FEM | [N] | 694 | 685 | 667 | 601 |
EXP | [N] | 639 | 628 | 619 | 553 | |
relative error | [%] | 7.93% | 8.32% | 7.20% | 7.99% |
7. Conclusions
- The study of the effect of the hole of the compressed plate in the critical state showed high agreement between the proposed test methods. No clear effect of the hole size on the form of buckling of the plate was observed. In all cases, one local half-wave was formed.
- On the other hand, a clear effect of the hole on the value of the critical load was determined. The maximum decrease in the value of the critical load equal to 14% was obtained for the plate with the S2 fiber layout, while the minimum decrease was 13% for the S1 plate. At the same time, the relative error between the numerical and experimental values of the critical load was no more than 9%.
- The post-critical work paths for the real plate and the FEM model show similar stability. This confirms the validity of the plate model developed in the numerical analysis, which made it possible to realize the issue of non-linear stability. For all analyzed plates, a change in the stiffness of the post-critical characteristic was observed with an increase in the size of the hole. The maximum decrease in the stiffness of the post-critical characteristic equal to 14% was obtained for the plate with the S1 layout, and the minimum equal to 10% was obtained for the plate with the layout S3.
- The study showed the effect of the layout of the fibers on the behavior of the compressed hole plates. It was observed that the S1 plate with composite layout [45|−45|90|0]s had more than three times lower strength compared to S2 [0|−45|45|90]s and S3 [0|90|0|90]s. This is evidenced by the displacement of the stiffest layer with the [0] layup to the plane of symmetry, thus weakening the S1 plate.
- The results of the critical and post-critical state analysis show the assumed trend. Numerical analysis was characterized by higher values compared to experimental ones. This is evidenced by the fact that the numerical analysis compared to the experiment represents ideal test conditions. At the same time, the satisfactory quantitative agreement of the results of the numerical analysis with the experimental results confirms the adequacy of the developed numerical model, which in the simulated case reproduces the behavior of the real plate with a hole.
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Correction Statement
References
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Sample | Laminate Layout |
---|---|
S1 | [45|−45|90|0|0|90|−45|45]T |
S2 | [0|−45|45|90|90|45|−45|0]T |
S3 | [0|90|0|90|90|0|90|0]T |
Tensile Strength | FTU | 0° | 1867 MPa |
90° | 26 MPa | ||
Tensile Modulus | E1 | 0° | 131.71 GPa |
E2 | 90° | 6.36 GPa | |
Poisson’s Ratio | ν12 | 0° | 0.32 |
Shear Strength | FSU | ±45° | 100.15 MPa |
Shear Modulus | G12 | ±45° | 4.18 GPa |
Compression Strength | FCU | 0° | 1531 MPa |
90° | 214 MPa |
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Wysmulski, P. Analysis of the Effect of an Open Hole on the Buckling of a Compressed Composite Plate. Materials 2024, 17, 1081. https://doi.org/10.3390/ma17051081
Wysmulski P. Analysis of the Effect of an Open Hole on the Buckling of a Compressed Composite Plate. Materials. 2024; 17(5):1081. https://doi.org/10.3390/ma17051081
Chicago/Turabian StyleWysmulski, Pawel. 2024. "Analysis of the Effect of an Open Hole on the Buckling of a Compressed Composite Plate" Materials 17, no. 5: 1081. https://doi.org/10.3390/ma17051081