Transient Post-Buckling of Microfluid-Conveying FG-CNTs Cylindrical Microshells Embedded in Kerr Foundation and Exposed to a 2D Magnetic Field
Abstract
:1. Introduction
2. Formulation
2.1. Displacement Field
2.2. Strain-Displacement Relations
2.3. Rotation and Curvature Tensors
2.4. Modified Couple Stress Model
3. Equations of Motion
3.1. Lorentz Force Applied to the Microshell
3.2. Force Due to the Magnetic Fluid
3.3. Hamilton’s Principle
4. Solution Procedure
5. Numerical Results
6. Conclusions
- The strength of the microshells may be enhanced by increasing the mean flow velocity, magnetic field parameter, Knudsen number, and CNT volume fraction, leading to an increment in the post-buckling paths.
- In contrast, an increase in the radius-to-thickness ratio, length-to-radius ratio, deflection, material length scale parameter, and Kerr foundation parameters results in a reduction in post-buckling strength.
- Moreover, the nonlinear dynamic deflection increases as the compressive load and material parameter increase, while a severe reduction in the deflection occurs by increasing the magnetic parameter and mean flow velocity.
- In the absence of the magnetic field, the material length scale parameter and Kerr foundation have no influence on the post-buckling behavior.
- The theoretical insights developed here have potential applications in the design of microscale systems, including MEMS/NEMS devices, flexible microfluidic pipelines, and biomedical microtubes, where understanding the combined effects of mechanical, fluidic, and magnetic loading is critical for optimizing performance and ensuring structural stability.
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
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Khdeir et al. [54] | Present | ||||
---|---|---|---|---|---|
Lamination | HST | FST | CST | ||
1 | 0.0804 | 0.0791 | 0.0866 | 0.0918 | |
2 | 0.1566 | 0.1552 | 0.1630 | 0.1692 | |
1 | 0.1097 | 0.1004 | 0.1479 | 0.1078 | |
2 | 0.1717 | 0.1779 | 0.2073 | 0.1960 | |
1 | 0.0984 | 0.0982 | 0.1235 | 0.1024 | |
10 layers | 2 | 0.1900 | 0.1899 | 0.1958 | 0.1856 |
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Sobhy, M. Transient Post-Buckling of Microfluid-Conveying FG-CNTs Cylindrical Microshells Embedded in Kerr Foundation and Exposed to a 2D Magnetic Field. Mathematics 2025, 13, 1518. https://doi.org/10.3390/math13091518
Sobhy M. Transient Post-Buckling of Microfluid-Conveying FG-CNTs Cylindrical Microshells Embedded in Kerr Foundation and Exposed to a 2D Magnetic Field. Mathematics. 2025; 13(9):1518. https://doi.org/10.3390/math13091518
Chicago/Turabian StyleSobhy, Mohammed. 2025. "Transient Post-Buckling of Microfluid-Conveying FG-CNTs Cylindrical Microshells Embedded in Kerr Foundation and Exposed to a 2D Magnetic Field" Mathematics 13, no. 9: 1518. https://doi.org/10.3390/math13091518
APA StyleSobhy, M. (2025). Transient Post-Buckling of Microfluid-Conveying FG-CNTs Cylindrical Microshells Embedded in Kerr Foundation and Exposed to a 2D Magnetic Field. Mathematics, 13(9), 1518. https://doi.org/10.3390/math13091518