Buckling Analysis on Resin Base Laminated Plate Reinforced with Uniform and Functional Gradient Distribution of Carbon Fiber in Thermal Environment
Abstract
:1. Introduction
2. Problem Formulation
3. Theoretical Formulation
3.1. Displacement Field Model
3.2. Buckling Equations
4. Result and Discussion
4.1. Validation
4.2. Parametric Studies
4.2.1. Effect of Carbon Fiber Volume Fraction
4.2.2. Effect of Thermal Environment
4.2.3. Effect of Geometrical Dimension of Plate
4.2.4. Effect of Lamination Angle
5. Conclusions
- (1)
- A larger corresponds to higher critical buckling loads; the buckling load decreases rapidly with the increase of the length-to-thickness ratio k2, then tends to become zero. The buckling loads are also significantly influenced by the lamination angle.
- (2)
- X-shaped FG distribution is more effective than the other two distributions for reinforcing the plate for a higher buckling load, and compared to uniform distribution, the buckling load increased by 47%.
- (3)
- A functionally graded composited plate with 10~15 individual layers stacked up can achieve a sufficient in-plane load.
- (4)
- Critical buckling loads decrease with a temperature increase ranging from 0 °C to 80 °C.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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k | a/b | Theory | |||||
---|---|---|---|---|---|---|---|
5 | 10 | 20 | 25 | 40 | |||
0 | 0.5 | Reddy [43] | 13.9000 | 18.1260 | 21.8780 | 22.8740 | 24.5900 |
Present | 13.9000 | 18.1265 | 21.8778 | 22.8738 | 24.5899 | ||
Ansys | 13.8666 | 17.6971 | 20.4871 | 20.9996 | 21.3372 | ||
1.0 | Reddy [43] | 5.6500 | 6.3470 | 6.9610 | 7.1240 | 7.4040 | |
Present | 5.6500 | 6.3470 | 6.9611 | 7.1238 | 7.4037 | ||
Ansys | 6.0568 | 6.6009 | 7.0363 | 7.1347 | 7.2598 | ||
1.5 | Reddy [43] | 5.2330 | 5.2770 | 5.3100 | 5.3180 | 5.3320 | |
Present | 5.2333 | 5.2768 | 5.3099 | 5.3182 | 5.3322 | ||
Ansys | 6.1796 | 5.8636 | 5.6220 | 5.5597 | 5.4452 | ||
1 | 0.5 | Reddy [43] | 11.1200 | 12.6940 | 13.9220 | 14.2480 | 14.7660 |
Present | 11.1200 | 12.6941 | 13.9222 | 14.2475 | 14.7661 | ||
Ansys | 11.6391 | 13.3583 | 13.7016 | 13.6693 | 13.3272 | ||
1.0 | Reddy [43] | 2.8250 | 3.1740 | 3.4840 | 3.5620 | 3.7020 | |
Present | 2.8250 | 3.1735 | 3.4806 | 3.5619 | 3.7019 | ||
Ansys | 3.0285 | 3.3005 | 3.5183 | 3.5675 | 3.6300 | ||
1.5 | Reddy [43] | 1.6100 | 1.6240 | 1.6340 | 1.6360 | 1.6410 | |
Present | 1.6103 | 1.6236 | 1.6338 | 1.6364 | 1.6407 | ||
Ansys | 1.7208 | 1.6935 | 1.6671 | 1.6590 | 1.6414 |
Plate | Tsung-Lin Wu [40] | Present |
---|---|---|
Alumina | 3.6498 | 3.6152 |
Aluminum | 0.67 | 0.6660 |
Material properties of fiber(carbon): | |||
= 230 GPa | = 23 GPa | = 9 GPa | |
= 0.2 | |||
Material properties of epoxy matrix: | |||
= (3.51 − 0.003 ΔT) GPa |
Lay-Up | UD | FG_X | FG_O | |
---|---|---|---|---|
Ansys | Present | |||
[90/0/−45/45]s, [90/0/45/−45]s, [0/90/−45/45]s, [0/90/45/−45]s | 50.78 | 51.46 | 69.11 ( + 34%) | 34.61 (−33%) |
[90/−45/45/0]s, [90/45/−45/0]s | 59.41 | 61.25 | 73.48 (+20%) | 41.43 (−32%) |
[90/−45/0/45]s, [90/45/0/−45]s | 54.63 | 57.99 | 77.40 (+33%) | 37.62 (−35%) |
[0/−45/90/45]s, [0/45/90/−45]s | 54.63 | 57.99 | 79.14 (+36%) | 37.62 (−35%) |
[0/−45/45/90]s, [0/45/−45/90]s | 59.41 | 61.25 | 81.87 (+34%) | 41.43 (−32%) |
[−45/90/45/0]s, [−45/0/45/90]s, [45/90/−45/0]s, [45/0/−45/90]s | 63.26 | 71.04 | 103.94 (+46%) | 38.72 (−45%) |
[−45/45/90/0]s, [−45/45/0/90]s, [45/−45/90/0]s, [45/−45/0/90]s | 74.24 | 77.57 | 113.97 (+47%) | 41.73 (−46%) |
0.05 | 0.1 | 0.15 | 0.2 | 0.25 | 0.3 | |
---|---|---|---|---|---|---|
Uniaxial compression | ||||||
Uniform | 14.78 | 21.17(+43%) | 27.59(+30%) | 34.05(+23%) | 40.55(+19%) | 47.11(+16%) |
FG-X | 17.84 | 27.34(+53%) | 36.93(+35%) | 46.65(+26%) | 56.51(+21%) | 66.58(+18%) |
FG-O | 11.73 | 15.04(+28%) | 18.37(+22%) | 21.72(+18%) | 25.09(+16%) | 28.48(+14%) |
Biaxial compression | ||||||
Uniform | 7.39 | 10.58(+43%) | 13.79(+30%) | 17.02(+23%) | 20.28(+19%) | 23.56(+16%) |
FG-X | 8.92 | 13.67(+53%) | 18.47(+35%) | 23.32(+26%) | 28.26(+21%) | 33.29(+18%) |
FG-O | 5.86 | 7.52(+28%) | 9.19(+22%) | 10.86(+18%) | 12.54(+15%) | 14.24(+14%) |
Distribution Pattern | Temperature Difference | k1 = 1 | k1 = 2.5 | ||
---|---|---|---|---|---|
γcr | Difference | γcr | Difference | ||
Uniform | ΔT = 0 ℃ | 5.35 | −17.57% | 5.39 | −2.60% |
ΔT = 40 ℃ | 4.41 | 5.24 | |||
FG-X | ΔT = 0 ℃ | 6.11 | −12.11% | 6.18 | −1.78% |
ΔT = 40 ℃ | 5.37 | 6.07 | |||
FG-O | ΔT = 0 ℃ | 3.95 | −31.65% | 3.93 | −5.09% |
ΔT = 40 ℃ | 2.70 | 3.73 |
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Zhou, X.; You, Q.; Gao, Y.; Hua, F.; Fu, W.; Huang, Q.; Wang, Y. Buckling Analysis on Resin Base Laminated Plate Reinforced with Uniform and Functional Gradient Distribution of Carbon Fiber in Thermal Environment. Polymers 2023, 15, 2086. https://doi.org/10.3390/polym15092086
Zhou X, You Q, Gao Y, Hua F, Fu W, Huang Q, Wang Y. Buckling Analysis on Resin Base Laminated Plate Reinforced with Uniform and Functional Gradient Distribution of Carbon Fiber in Thermal Environment. Polymers. 2023; 15(9):2086. https://doi.org/10.3390/polym15092086
Chicago/Turabian StyleZhou, Xiaoqiang, Qingquan You, Yuan Gao, Fenfei Hua, Wanbiao Fu, Qingyang Huang, and Yuanfang Wang. 2023. "Buckling Analysis on Resin Base Laminated Plate Reinforced with Uniform and Functional Gradient Distribution of Carbon Fiber in Thermal Environment" Polymers 15, no. 9: 2086. https://doi.org/10.3390/polym15092086