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Thermal Buckling Analysis of Size-Dependent FG Nanobeams Based on the Third-Order Shear Deformation Beam Theory

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Abstract

In this paper, the thermal effects on the buckling of functionally graded (FG) nano-beams subjected to various types of thermal loading including uniform, linear and non-linear temperature changes are investigated based on the nonlocal third-order shear deformation beam theory. The material properties of FG nanobeam are supposed to vary gradually along the thickness direction according to the power-law form. The governing equations are derived through Hamilton’s principle and solved analytically. Comparison examples are performed to verify the present results. Obtained results are presented for thermal buckling analysis of FG nanobeams such as the effects of the power-law index, nonlocal parameter, slenderness ratio and thermal loading in detail.

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References

  1. Eringen, A.Cemal, Nonlocal polar elastic continua. International Journal of Engineering Science, 1972, 10(1): 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  2. Eringen, A.Cemal, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics, 1983, 54(9): 4703–4710.

    Article  Google Scholar 

  3. Peddieson, John, George, R., Buchanan and Richard, P.McNitt, Application of nonlocal continuum models to nanotechnology. International Journal of Engineering Science, 2003, 41(3) : 305–312.

    Article  Google Scholar 

  4. Reddy, J.N., Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science, 2007, 45(2): 288–307.

    Article  MATH  Google Scholar 

  5. Wang, Q. and Liew, K.M., Application of nonlocal continuum mechanics to static analysis of micro-and nano-structures. Physics Letters A, 2007, 363(3): 236–242.

    Article  Google Scholar 

  6. Aydogdu, Metin, A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration. Physica E: Low-dimensional Systems and Nanostructures, 2009, 41(9): 1651–1655.

    Article  Google Scholar 

  7. Phadikar, J.K. and Pradhan, S.C., Variational formulation and finite element analysis for nonlocal elastic nanobeams and nanoplates. Computational Materials Science, 2010, 49(3): 492–499.

    Article  Google Scholar 

  8. Pradhan, S.C. and Murmu, T., Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever. Physica E: Low-dimensional Systems and Nanostructures, 2010, 42(7): 1944–1949.

    Article  Google Scholar 

  9. Civalek, Ömer, Cigdem Demir and Bekir Akgöz, Free vibration and bending analyses of cantilever microtubules based on nonlocal continuum model. Math. Comput. Appl, 2010, 15(2): 289–298.

    MathSciNet  MATH  Google Scholar 

  10. Civalek, Ömer and Çiǧem Demir, Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory. Applied Mathematical Modelling, 2011, 35(5): 2053–2067.

    Article  MathSciNet  MATH  Google Scholar 

  11. Thai, Huu-Tai, A nonlocal beam theory for bending, buckling, and vibration of nanobeams. International Journal of Engineering Science, 2012, 52: 56–64.

    Article  MathSciNet  Google Scholar 

  12. Şmşk, Mesut, Large amplitude free vibration of nanobeams with various boundary conditions based on the nonlocal elasticity theory. Composites Part B: Engineering, 2014, 56: 621–628.

    Article  Google Scholar 

  13. Ansari, R., Gholami, R. and Rouhi, H., Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory. Composite Structures, 2015, 126: 216–226.

    Article  Google Scholar 

  14. Eltaher, M.A., Samir, A.Emam and Mahmoud, F.F., Free vibration analysis of functionally graded size-dependent nanobeams. Applied Mathematics and Computation, 2012, 218(14): 7406–7420.

    Article  MathSciNet  MATH  Google Scholar 

  15. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F., Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams. Composite Structures, 2013, 99: 193–201.

    Article  Google Scholar 

  16. Eltaher, M.A., Samir, A.Emam and Mahmoud, F.F., Static and stability analysis of nonlocal functionally graded nanobeams. Composite Structures, 2013b, 96: 82–88.

    Article  Google Scholar 

  17. Şmşk, M. and Yurtcu, H.H., Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Composite Structures, 2013, 97: 378–386.

    Article  Google Scholar 

  18. Rahmani, O. and Pedram, O., Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory. International Journal of Engineering Science, 2014, 77: 55–70.

    Article  MathSciNet  Google Scholar 

  19. Ebrahimi, Farzad, et al., Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams. Journal of Mechanical Science and Technology, 2015a, 29(3): 1207–1215.

    Article  Google Scholar 

  20. Ebrahimi, Farzad and Erfan Salari, Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method. Composites Part B: Engineering, 2015b, 79: 156–169.

    Article  Google Scholar 

  21. Ebrahimi, Farzad and Erfan Salari, A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position. CMES: Computer Modeling in Engineering & Sciences, 2015, 105(2): 151–181.

    Google Scholar 

  22. Ebrahimi, Farzad and Erfan Salari, Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions. Composites Part B: Engineering, 2015, 78: 272–290.

    Article  Google Scholar 

  23. 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, 2016, 41(5): 1679–1690.

    Article  MathSciNet  Google Scholar 

  24. Touratier, M., An efficient standard plate theory. International Journal of Engineering Science, 1991, 29(8): 901–916.

    Article  MATH  Google Scholar 

  25. Ed.Yeram Sarkis Touloukian.Macmillan, Thermophysical Properties Research Center. Thermophysical properties of high temperature solid materials. Elements.-Pt.1, 1967, 1.

  26. Rahmani, O. and Jandaghian, A.A., Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory. Applied Physics A, 2015, 119(3): 1019–1032.

    Article  Google Scholar 

  27. 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, 2016, 141: 203–212.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran

    Farzad Ebrahimi & Mohammad Reza Barati

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  1. Farzad Ebrahimi
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  2. Mohammad Reza Barati
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Correspondence to Farzad Ebrahimi.

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Ebrahimi, F., Barati, M.R. Thermal Buckling Analysis of Size-Dependent FG Nanobeams Based on the Third-Order Shear Deformation Beam Theory. Acta Mech. Solida Sin. 29, 547–554 (2016). https://doi.org/10.1016/S0894-9166(16)30272-5

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  • DOI: https://doi.org/10.1016/S0894-9166(16)30272-5

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