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Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams

Published online by Cambridge University Press:  24 May 2016

F. Ebrahimi  and
M. R. Barati
F. Ebrahimi*
Affiliation:
Mechanical Engineering DepartmentFaculty of EngineeringImam Khomeini International UniversityQazvin, Iran
M. R. Barati
Affiliation:
Mechanical Engineering DepartmentFaculty of EngineeringImam Khomeini International UniversityQazvin, Iran
*
*Corresponding author ([email protected])

Abstract

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The present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.

Keywords

Magneto-electro-thermo-elastic FG nanobeamBucklingNonlocal elasticity theoryHigher order beam theory
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 1 , February 2017 , pp. 23 - 33
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

References

1. Jiang, A. and Ding, H., “Analytical Solutions to Magneto-Electro-Elastic Beams,” Structural Engineering and Mechanics, 18, pp. 195–209 (2004).CrossRefGoogle Scholar
2. Chen, W. Q., Lee, K. Y. and Ding, H. J., “On Free Vibration of Non-Homogeneous Transversely Isotropic Magneto-Electro-Elastic Plates,” Journal of Sound and Vibration, 279, pp. 237–251 (2005).Google Scholar
3. Annigeri, A. R., Ganesan, N. and Swarnamani, S., “Free Vibration Behaviour of Multiphase and Layered Magneto-Electro-Elastic Beam,” Journal of Sound and Vibration, 299, pp. 44–63 (2007).Google Scholar
4. Kumaravel, A., Ganesan, N. and Sethuraman, R., “Buckling and Vibration Analysis of Layered and Multiphase Magneto-Electro-Elastic Beam Under Thermal Environment,” Multidiscipline Modeling in Materials and Structures, 3, pp. 461–476 (2007).Google Scholar
5. Daga, A., Ganesan, N. and Shankar, K., “Transient Dynamic Response of Cantilever Magneto-Electro-Elastic Beam Using Finite Elements,” International Journal for Computational Methods in Engineering Science and Mechanics, 10, pp. 173–185 (2009).Google Scholar
6. Liu, M. F. and Chang, T. P., “Closed form Expression for the Vibration Problem of a Transversely Isotropic Magneto-Electro-Elastic Plate,” Journal of Applied Mechanics, 77, p. 024502 (2010).Google Scholar
7. Razavi, S. and Shooshtari, A., “Nonlinear Free Vibration of Magneto-Electro-Elastic Rectangular Plates,” Composite Structures, 119, pp. 377–384 (2015).Google Scholar
8. Xin, L. and Hu, Z., “Free Vibration of Layered Magneto-Electro-Elastic Beams by SS-DSC Approach,” Composite Structures, 125, pp. 96–103 (2015).Google Scholar
9. Pan, E. and Han, F., “Exact Solution for Functionally Graded and Layered Magneto-Electro-Elastic Plates,” International Journal of Engineering Science, 43, pp. 321–339 (2005).Google Scholar
10. Huang, D. J., Ding, H. J. and Chen, W. Q., “Analytical Solution for Functionally Graded Magneto-Electro-Elastic Plane Beams,” International Journal of Engineering Science, 45, pp. 467–485 (2007).Google Scholar
11. Wu, C. P. and Tsai, Y. H., “Static Behavior of Functionally Graded Magneto-Electro-Elastic Shells Under Electric Displacement and Magnetic Flux,” International Journal of Engineering Science, 45, pp. 744–769 (2007).CrossRefGoogle Scholar
12. Li, X. Y., Ding, H. J. and Chen, W. Q., “Three-Dimensional Analytical Solution for Functionally Graded Magneto-Electro-Elastic Circular Plates Subjected to Uniform Load,” Composite Structures, 83, pp. 381–390 (2008).Google Scholar
13. Kattimani, S. C. and Ray, M. C., “Control of Geometrically Nonlinear Vibrations of Functionally Graded Magneto-Electro-Elastic Plates,” International Journal of Mechanical Sciences, pp. 154–167 (2015).Google Scholar
14. Sladek, J., Sladek, V., Krahulec, S., Chen, C. S. and Young, D. L., “Analyses of Circular Magnetoelectroelastic Plates with Functionally Graded Material Properties,” Mechanics of Advanced Materials and Structures, 22, pp. 479–489 (2015).Google Scholar
15. Li, C., “A Nonlocal Analytical Approach for Torsion of Cylindrical Nanostructures and the Existence of Higher-Order Stress and Geometric Boundaries,” Composite Structures, 118, pp. 607–621 (2014).CrossRefGoogle Scholar
16. Eringen, A. C. and Edelen, D. G. B., “On Nonlocal Elasticity,” International Journal of Engineering Science, 10, pp. 233–248 (1972).Google Scholar
17. Eringen, A. C., “Nonlocal Polar Elastic Continua,” International Journal of Engineering Science, 10, pp. 1–16 (1972).CrossRefGoogle Scholar
18. Barati, M. R., Zenkour, A. M. and Shahverdi, H., “Thermo-Mechanical Buckling Analysis of Embedded Nanosize FG Plates in Thermal Environments Via an Inverse Cotangential Theory,” Composite Structures, 141, pp. 203–212 (2016).Google Scholar
19. Li, C., Yao, L., Chen, W. and Li, S., “Comments on Nonlocal Effects in Nano-Cantilever Beams,” International Journal of Engineering Science, 87, pp. 47–57 (2015).Google Scholar
20. Li, C., Zheng, Z. J., Yu, J. L. and Lim, C. W., “Static Analysis of Ultra-Thin Beams Based on a Semi-Continuum Model,” Acta Mechanica Sinica, 27, pp. 713–719 (2011).Google Scholar
21. Li, C., Li, S., Yao, L. and Zhu, Z., “Nonlocal Theoretical Approaches and Atomistic Simulations for Longitudinal Free Vibration of Nanorods/Nanotubes and Verification of Different Nonlocal Models,” Applied Mathematical Modelling, 39, pp. 4570–4585 (2015).CrossRefGoogle Scholar
22. Şimşek, M. and Yurtcu, H. H., “Analytical Solutions for Bending and Buckling of Functionally Graded Nanobeams Based on the Nonlocal Timoshenko Beam Theory,” Composite Structures, 97, pp. 378–386 (2013).Google Scholar
23. Rahmani, O. and Jandaghian, A. A., “Buckling Analysis of Functionally Graded Nanobeams Based on a Nonlocal Third-Order Shear Deformation Theory,” Applied Physics A, 119, pp. 1019–1032 (2015).Google Scholar
24. Zemri, A., Houari, M. S. A., Bousahla, A. A. and Tounsi, A., “A Mechanical Response of Functionally Graded Nanoscale Beam: An Assessment of a Refined Nonlocal Shear Deformation Theory Beam Theory,” Structural Engineering and Mechanics, 54, pp. 693–710 (2015).Google Scholar
25. Ebrahimi, F. and Barati, M. R., “A Nonlocal Higher-Order Shear Deformation Beam Theory for Vibration Analysis of Size-Dependent Functionally Graded Nanobeams,” Arabian Journal for Science and Engineering, 40, pp. 1–12 (2015).Google Scholar
26. Ebrahimi, F. and Salari, E., “Thermal Buckling and Free Vibration Analysis of Size Dependent Timoshenko FG Nanobeams in Thermal Environments,” Composite Structures, 128, pp. 363–380 (2015).Google Scholar
27. Ke, L. L. and Wang, Y. S., “Free Vibration of Size-Dependent Magneto-Electro-Elastic Nanobeams Based on the Nonlocal Theory,” Physica E: Low-Dimensional Systems and Nanostructures, 63, pp. 52–61 (2014).Google Scholar
28. Ke, L. L., Wang, Y. S., Yang, J. and Kitipornchai, S., “Free Vibration of Size-Dependent Magneto-Electro-Elastic Nanoplates Based on the Nonlocal Theory,” Acta Mechanica Sinica, 30, pp. 516–525 (2014).CrossRefGoogle Scholar
29. Li, Y. S., Cai, Z. Y. and Shi, S. Y., “Buckling and Free Vibration of Magnetoelectroelastic Nanoplate Based on Nonlocal Theory,” Composite Structures, 111, pp. 522–529 (2014).Google Scholar
30. Ansari, R., Hasrati, E., Gholami, R. and Sadeghi, F., “Nonlinear Analysis of Forced Vibration of Nonlocal Third-Order Shear Deformable Beam Model of Magneto-Electro-Thermo Elastic Nanobeams,” Composites Part B: Engineering, 83, pp. 226–241 (2015).Google Scholar
31. Wu, B., Zhang, C., Chen, W. and Zhang, C., “Surface Effects on Anti-Plane Shear Waves Propagating in Magneto-Electro-Elastic Nanoplates,” Smart Materials and Structures, 24, p. 095017 (2015).CrossRefGoogle Scholar
32. Wang, Y. G., Lin, W. H., Zhou, C. L. and Liu, R. X., “Thermal Postbuckling and Free Vibration of Extensible Microscale Beams Based on Modified Couple Stress Theory,” Journal of Mechanics, 31, pp. 37–46 (2015).Google Scholar
33. Ootao, Y. and Tanigawa, Y., “Transient Analysis of Multilayered Magneto-Electro-Thermoelastic Strip Due to Nonuniform Heat Supply,” Composite Structures, 68, pp. 471–480 (2005).Google Scholar
34. Na, K. S. and Kim, J. H., “Three-Dimensional Thermal Buckling Analysis of Functionally Graded Materials,” Composites Part B: Engineering, 35, pp. 429–437 (2004).CrossRefGoogle Scholar
35. Ramirez, F., Heyliger, P. R. and Pan, E., “Discrete Layer Solution to Free Vibrations of Functionally Graded Magneto-Electro-Elastic Plates,” Mechanics of Advanced Materials and Structures, 13, pp. 249–266 (2006).Google Scholar