Thermal buckling analysis of a functionally graded microshell based on higher-order shear deformation and modified couple stress theories

References

• Anitescu, C., A. Elena, N. Alajlan, and T. Rabczuk 2019. Artificial neural network methods for the solution of second order boundary value problems. Computers, Materials and Continua 59:345–59. doi:10.32604/cmc.2019.06641.
   Web of Science ®Google Scholar
• Ansari Sadrabadi, S., A. Nayebi, and G. H. Rahimi. 2016. Behavior of FGM spherical vessels under internal pressure and temperature difference. Journal of Mechanical Engineering Amirkabir (Amirkabir) 47 (2):43–50. https://www.sid.ir/en/journal/ViewPaper.aspx?id=538958.
   Google Scholar
• Ansari Sadrabadi, S., and G. H. Rahimi. 2014. Yield onset of thermo-mechanical loading of FGM thick walled cylindrical pressure vessels. International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering 8 (7):1317–21. https://scholar.google.com/scholar?oi=bibs&cluster=1359836620809388720&btnI=1&hl=en.
   Google Scholar
• Ansari Sadrabadi, S., and G. H. Rahimi. 2016. Elasto-plastic behavior analysis and yield onset in FG cylindrical tubes under mechanical and thermal loads. Modares Mechanical Engineering 16 (2):159–66. https://www.sid.ir/en/journal/ViewPaper.aspx?id=502934.
   Google Scholar
• Ansari Sadrabadi, S., G. H. H. Rahimi, R. Citarella, J. Shahbazi Karami, R. Sepe, and R. Esposito. 2017. Analytical solutions for yield onset achievement in FGM thick walled cylindrical tubes undergoing thermomechanical loads. Composites Part B: Engineering 116:211–23. doi:10.1016/j.compositesb.2017.02.023.
   Web of Science ®Google Scholar
• Babaei, H., and M. R. Eslami. 2020. Nonlinear bending analysis of size-dependent FG porous microtubes in thermal environment based on modified couple stress theory. Mechanics Based Design of Structures and Machines 1–22. doi:10.1080/15397734.2020.1784202.
   Web of Science ®Google Scholar
• Babaei, H., Y. Kiani, and M. Reza Eslami. 2019. Thermal buckling and post-buckling analysis of geometrically imperfect FGM clamped tubes on nonlinear elastic foundation. Applied Mathematical Modelling 71:12–30. doi:10.1016/j.apm.2019.02.009.
   Web of Science ®Google Scholar
• Bagheri, E., and M. Asghari. 2019. Elasticity formulation for motion equations of couple stress based micro-rotating disks with varying speeds. Mechanics Based Design of Structures and Machines 49 (1):1–19. doi:10.1080/15397734.2019.1652833.
   Web of Science ®Google Scholar
• Chen, X., X. Zhang, Y. Lu, and Y. Li. 2019. Static and dynamic analysis of the postbuckling of bi-directional functionally graded material microbeams. International Journal of Mechanical Sciences 151:424–43. doi:10.1016/j.ijmecsci.2018.12.001.
   Web of Science ®Google Scholar
• Demirhan, N., and B. Kanber. 2013. Finite element analysis of frictional contacts of FGM coated elastic members. Mechanics Based Design of Structures and Machines 41 (4):383–98. doi:10.1080/15397734.2012.722882.
   Web of Science ®Google Scholar
• Dong, Z., X. Zhang, W. Shi, H. Zhou, H. Lei, and J. Liang. 2018. Study of size effect on microstructure and mechanical properties of AlSi10Mg samples made by selective laser melting. Materials 11 (12):2463. doi:10.3390/ma11122463.
   PubMed Web of Science ®Google Scholar
• Fares, M. E., M. K. Elmarghany, and D. Atta. 2009. An efficient and simple refined theory for bending and vibration of functionally graded plates. Composite Structures 91 (3):296–305. doi:10.1016/j.compstruct.2009.05.008.
   Web of Science ®Google Scholar
• Gholami, R., A. Darvizeh, R. Ansari, and M. Hosseinzadeh. 2014. Size-dependent axial buckling analysis of functionally graded circular cylindrical microshells based on the modified strain gradient elasticity theory. Meccanica 49 (7):1679–95. doi:10.1007/s11012-014-9944-7.
   Web of Science ®Google Scholar
• Golchi, M., M. Talebitooti, and R. Talebitooti. 2019. Thermal buckling and free vibration of FG truncated conical shells with stringer and ring stiffeners using differential quadrature method. Mechanics Based Design of Structures and Machines 47 (3):255–82. doi:10.1080/15397734.2018.1545588.
   Web of Science ®Google Scholar
• Hadjesfandiari, A. R., and G. F. Dargush. 2011. Couple stress theory for solids. International Journal of Solids and Structures 48 (18):2496–510. doi:10.1016/j.ijsolstr.2011.05.002.
   Web of Science ®Google Scholar
• Hadjesfandiari, A. R., and G. F. Dargush. 2016. Couple stress theories: Theoretical underpinnings and practical aspects from a new energy perspective. 1–45. http://arxiv.org/abs/1611.10249.
   Google Scholar
• Han, Q., Z. Wang, D. H. Nash, and P. Liu. 2017. Thermal buckling analysis of cylindrical shell with functionally graded material coating. Composite Structures 181:171–82. doi:10.1016/j.compstruct.2017.08.085.
   Web of Science ®Google Scholar
• Karma, A., and D. Tourret. 2016. Atomistic to continuum modeling of solidification microstructures. Current Opinion in Solid State and Materials Science 20 (1):25–36. doi:10.1016/j.cossms.2015.09.001.
   Web of Science ®Google Scholar
• Kim, J., K. K. Żur, and J. N. Reddy. 2019. Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates. Composite Structures 209:879–88. doi:10.1016/j.compstruct.2018.11.023.
   Web of Science ®Google Scholar
• Lam, D. C. C., F. Yang, A. C. M. Chong, J. Wang, and P. Tong. 2003. Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids 51 (8):1477–508. doi:10.1016/S0022-5096(03)00053-X.
   Web of Science ®Google Scholar
• Lei, J., Y. He, S. Guo, Z. Li, and D. Liu. 2017. Thermal buckling and vibration of functionally graded sinusoidal microbeams incorporating nonlinear temperature distribution using DQM. Journal of Thermal Stresses 40 (6):665–89. doi:10.1080/01495739.2016.1258602.
   Web of Science ®Google Scholar
• Liu, D., Y. He, X. Tang, H. Ding, P. Hu, and P. Cao. 2012. Size effects in the torsion of microscale copper wires: Experiment and analysis. Scripta Materialia 66 (6):406–9. doi:10.1016/j.scriptamat.2011.12.003.
   Web of Science ®Google Scholar
• Liu, Y., and Y. Wang. 2019. Size-dependent free vibration and buckling of three-dimensional graphene foam microshells based on modified couple stress theory. Materials 12 (5):729. doi:10.3390/ma12050729.
   PubMed Web of Science ®Google Scholar
• Mehditabar, A., S. Ansari Sadrabadi, R. Sepe, E. Armentani, J. Walker, and R. Citarella. 2020. Influences of material variations of functionally graded pipe on the Bree diagram. Applied Sciences 10 (8):2936. doi:10.3390/app10082936.
   Google Scholar
• Mehditabar, A., and G. H. Rahimi. 2019. Numerical prediction of the elastoplastic response of FG tubes using nonlinear kinematic hardening rule with power-law function model under thermomechanical loadings. Engineering Computations 36 (1):103–25. doi:10.1108/EC-02-2018-0102.
   Web of Science ®Google Scholar
• Mehditabar, A., G. H. H. Rahimi, and S. A. Sadrabadi. 2017. Three-dimensional magneto-thermo-elastic analysis of functionally graded cylindrical shell. Applied Mathematics and Mechanics 38 (4):479–94. doi:10.1007/s10483-017-2186-6.
   Google Scholar
• Nayebi, A., and S. Ansari Sadrabadi. 2013. FGM elastoplastic analysis under thermomechanical loading. International Journal of Pressure Vessels and Piping 111–112:12–20. doi:10.1016/j.ijpvp.2013.04.028.
   Web of Science ®Google Scholar
• Qi, L., G. Fu, and S. Zhou. 2019. A flexoelectric spherical microshell model incorporating the strain gradient effect. Applied Mathematical Modelling 75:692–708. doi:10.1016/j.apm.2019.05.034.
   Web of Science ®Google Scholar
• Rabczuk, T., P. M. A. Areias, and T. Belytschko. 2007. A meshfree thin shell method for non-linear dynamic fracture. International Journal for Numerical Methods in Engineering 72 (5):524–48. doi:10.1002/nme.2013.
   Web of Science ®Google Scholar
• Reddy, J. N. 2006. Theory and analysis of elastic plates and shells. Baco Raton, FL: CRC Press. doi:10.1201/9780849384165.
   Google Scholar
• Reddy, J. N., and J. Kim. 2012. A nonlinear modified couple stress-based third-order theory of functionally graded plates. Composite Structures 94 (3):1128–43. doi:10.1016/j.compstruct.2011.10.006.
   Web of Science ®Google Scholar
• Sabzikar Boroujerdy, M., and M. R. Eslami. 2013. Thermal buckling of piezo-FGM shallow spherical shells. Meccanica 48 (4):887–99. doi:10.1007/s11012-012-9642-2.
   Web of Science ®Google Scholar
• Sahmani, S., and R. Ansari. 2013. Size-dependent buckling analysis of functionally graded third-order shear deformable microbeams including thermal environment effect. Applied Mathematical Modelling 37 (23):9499–515. doi:10.1016/j.apm.2013.04.051.
   Web of Science ®Google Scholar
• Sahmani, S., R. Ansari, R. Gholami, and A. Darvizeh. 2013. Dynamic stability analysis of functionally graded higher-order shear deformable microshells based on the modified couple stress elasticity theory. Composites Part B: Engineering 51:44–53. doi:10.1016/j.compositesb.2013.02.037.
   Web of Science ®Google Scholar
• Samaniego, E., C. Anitescu, S. Goswami, V. M. Nguyen-Thanh, H. Guo, K. Hamdia, X. Zhuang, and T. Rabczuk. 2020. An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications. Computer Methods in Applied Mechanics and Engineering 362. doi:10.1016/j.cma.2019.112790.
   Web of Science ®Google Scholar
• Shaat, M. 2017. A general nonlocal theory and its approximations for slowly varying acoustic waves. International Journal of Mechanical Sciences 130:52–63. doi:10.1016/j.ijmecsci.2017.05.038.
   Web of Science ®Google Scholar
• Shahsiah, R., and M. R. Eslami. 2003. Thermal buckling of functionally graded cylindrical shell. Journal of Thermal Stresses 26 (3):277–94. doi:10.1080/713855892.
   Web of Science ®Google Scholar
• Shen, H. S. 2012. Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells. Composites Part B: Engineering 43 (3):1030–8. doi:10.1016/j.compositesb.2011.10.004.
   Web of Science ®Google Scholar
• Shu, C. 2000. Differential quadrature and its application in engineering. London: Springer Verlag. doi:10.1007/978-1-4471-0407-0.
   Google Scholar
• Soldatos, K. P., and T. Timarci. 1993. A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories. Composite Structures 25 (1–4):165–71. doi:10.1016/0263-8223(93)90162-J.
   Web of Science ®Google Scholar
• Tufekci, E., U. Eroglu, and S. A. Aya. 2016. Exact solution for in-plane static problems of circular beams made of functionally graded materials. Mechanics Based Design of Structures and Machines 44 (4):476–94. doi:10.1080/15397734.2015.1121398.
   Web of Science ®Google Scholar
• Vu-Bac, N., T. X. Duong, T. Lahmer, X. Zhuang, R. A. Sauer, H. S. Park, and T. Rabczuk. 2018. A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures. Computer Methods in Applied Mechanics and Engineering 331:427–55. doi:10.1016/j.cma.2017.09.034.
   Web of Science ®Google Scholar
• Vu-Bac, N., T. Lahmer, X. Zhuang, T. Nguyen-Thoi, and T. Rabczuk. 2016. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software 100:19–31. doi:10.1016/j.advengsoft.2016.06.005.
   Web of Science ®Google Scholar
• Wang, X., J. Chunhua, and Y. Zhangxian. 2020a. Free vibration of FGM annular sectorial plates with arbitrary boundary supports and large sector angles. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2020.1717342.
   Web of Science ®Google Scholar
• Wang, Y., X. Ke, F. Tairan, and Z. Wei. 2020b. A unified modified couple stress model for size-dependent free vibrations of FG cylindrical microshells based on high-order shear deformation theory. European Physical Journal Plus, 135, 71. doi:10.1140/epjp/s13360-019-00012-3.
   Web of Science ®Google Scholar
• Wang, Y., Q. Han, D. H. Nash, P. Liu, and D. Hu. 2018. Investigation of imperfect effect on thermal buckling of cylindrical shell with FGM coating. European Journal of Mechanics, A/Solids 69:221–30. doi:10.1016/j.euromechsol.2018.01.004.
   Web of Science ®Google Scholar
• Wu, C.-P., and H.-Y. Huang. 2020. A semianalytical finite element method for stress and deformation analyses of bi-directional functionally graded truncated conical shells. Mechanics Based Design of Structures and Machines 48 (4):433–58. doi:10.1080/15397734.2019.1636657.
   Web of Science ®Google Scholar
• Wu, L., Z. Jiang, and J. Liu. 2005. Thermoelastic stability of functionally graded cylindrical shells. Composite Structures 70 (1):60–8. doi:10.1016/j.compstruct.2004.08.012.
   Web of Science ®Google Scholar
• Wu, C., Ping, and L. Y. Chiu. 2020. Three-dimensional free vibration analysis of rotating sandwich functionally graded truncated conical shells under various boundary conditions. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2020.1864400.
   Web of Science ®Google Scholar
• Yu, T., H. Hu, J. Zhang, and T. Q. Bui. 2019. Isogeometric analysis of size-dependent effects for functionally graded microbeams by a non-classical quasi-3D theory. Thin-Walled Structures 138:1–14. doi:10.1016/j.tws.2018.12.006.
   Web of Science ®Google Scholar
• Yuan, Y., K. Zhao, Y. Zhao, S. Sahmani, and B. Safaei. 2020. Couple stress-based nonlinear buckling analysis of hydrostatic pressurized functionally graded composite conical microshells. Mechanics of Materials 148, 103507. doi:10.1016/j.mechmat.2020.103507.
   Web of Science ®Google Scholar