Meshfree analysis of functionally graded plates with a novel four-unknown arctangent exponential shear deformation theory

References

• Amirpour, M., S. Bickerton, E. Calius, R. Das, and B. Mace. 2019. Numerical and experimental study on deformation of 3D-printed polymeric functionally graded plates: 3D-digital image correlation approach. Composite Structures 211:481–9. doi:10.1016/j.compstruct.2019.01.014.
   Web of Science ®Google Scholar
• Amirpour, M., S. Bickerton, E. Calius, B. Mace, and R. Das. 2018. Numerical and experimental study on free vibration of 3D-printed polymeric functionally graded plates. Composite Structures 189:192–205. doi:10.1016/j.compstruct.2018.01.056.
   Web of Science ®Google Scholar
• Baferani, A. H., A. R. Saidi, and E. Jomehzadeh. 2011. An exact solution for free vibration of thin functionally graded rectangular plates. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225 (3):526–3. doi:10.1243/09544062JMES2171.
   Web of Science ®Google Scholar
• Bessaim, A., M. S. A. Houari, A. Tounsi, S. R. Mahmoud, and E. A. Adda Bedia. 2013. A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets. Journal of Sandwich Structures and Materials 15 (6):671–703. doi:10.1177/1099636213498888.
   Web of Science ®Google Scholar
• Bui, Q. T., N. T. Nguyen, and D. H. Nguyen. 2009. A moving kriging interpolation-based meshless method for numerical simulation of Kirchhoff plate problems. International Journal for Numerical Methods in Engineering 77 (10):1371–95. doi:10.1002/nme.2462.
   Web of Science ®Google Scholar
• Carrera, E., S. Brischetto, M. Cinefra, and M. Soave. 2011. Effects of thickness stretching in functionally graded plates and shells. Composites Part B: Engineering 42 (2):123–33. doi:10.1016/j.compositesb.2010.10.005.
   Web of Science ®Google Scholar
• Cheshmeh, E., M. Karbon, A. Eyvazian, D. W. Jung, M. Habibi, and M. Safarpour. 2020. Buckling and vibration analysis of FG-CNTRC plate subjected to thermo-mechanical load based on higher order shear deformation theory. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2020.1744005.
   Web of Science ®Google Scholar
• Chu, F., J. He, L. Wang, and Z. Zhong. 2016. Buckling analysis of functionally graded thin plate with in-plane material inhomogeneity. Engineering Analysis with Boundary Elements 65:112–25. doi:10.1016/j.enganabound.2016.01.007.
   Web of Science ®Google Scholar
• Dastjerdi, R. M., S. Rashahmadi, and S. A. Meguid. 2020. Electro-mechanical performance of smart piezoelectric nanocomposite plates reinforced by zinc oxide and gallium nitride nanowires. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2020.1766496.
   Web of Science ®Google Scholar
• Ebrahimi, F., A. Rastgoo, and A. A. Atai. 2009. A theoretical analysis of smart moderately thick shear deformable annular functionally graded plate. European Journal of Mechanics: A/Solids 28 (5):962–73. doi:10.1016/j.euromechsol.2008.12.008.
   Web of Science ®Google Scholar
• Farzad, E., M. Nouraei, and A. Dabbagh. 2020. Modeling vibration behavior of embedded graphene-oxide powder-reinforced nanocomposite plates in thermal environment. Mechanics Based Design of Structures and Machines 48 (2):217–40. doi:10.1080/15397734.2019.1660185.
   Web of Science ®Google Scholar
• Garg, A., H. D. Chalak, and A. Chakrabarti. 2020. Bending analysis of functionally graded sandwich plates using HOZT including transverse displacement effects. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2020.1814157.
   Web of Science ®Google Scholar
• Hachemi, M., and S. M. H. Cherif. 2020. Free vibration of composite laminated plate with complicated cutout. Mechanics Based Design of Structures and Machines 48 (2):192–216. doi:10.1080/15397734.2019.1633341.
   Web of Science ®Google Scholar
• Hosseini-Hashemi, S., M. Fadaee, and M. Es'haghi. 2010. A novel approach for in-plane/out-of-plane frequency analysis of functionally graded circular/annular plates. International Journal of Mechanical Sciences 52 (8):1025–35. doi:10.1016/j.ijmecsci.2010.04.009.
   Web of Science ®Google Scholar
• Karama, M., K. S. Afaq, and S. Mistou. 2003. Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity. International Journal of Solids and Structures 40 (6):1525–46. doi:10.1016/S0020-7683(02)00647-9.
   Web of Science ®Google Scholar
• Kiendl, J., Y. Bazilevs, M. C. Hsu, R. Wuchner, and K. U. Bletzinger. 2010. The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches. Computer Methods in Applied Mechanics and Engineering 199 (37–40):2403–16. doi:10.1016/j.cma.2010.03.029.
   Web of Science ®Google Scholar
• Kirchhoff, G. 1850. Über das gleichgewicht und die bewegung einer elastischen scheibe [On the balance and the movement of a resilient disc. Journal Für Die Reine Und Angewandte Mathematik 40:51–88. doi:10.1515/crll.1850.40.5.
   Google Scholar
• Lee, Y. Y., X. Zhao, and K. M. Liew. 2009. Thermoelastic analysis of functionally graded plates using the element-free kp-Ritz method. Smart Materials and Structures 18 (3):035007. doi:10.1088/0964-1726/18/3/035007.
   Web of Science ®Google Scholar
• Li, Q., V. P. Iu, and K. P. Kou. 2008. Three-dimensional vibration analysis of functionally graded material sandwich plates. Journal of Sound and Vibration 311 (1–2):498–515. doi:10.1016/j.jsv.2007.09.018.
   Web of Science ®Google Scholar
• Li, X. Y., H. J. Ding, and W. Q. Chen. 2008. Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load QRK. International Journal of Solids and Structures 45 (1):191–210. doi:10.1016/j.ijsolstr.2007.07.023.
   Web of Science ®Google Scholar
• Lieu, Q. X., S. Lee, J. Kang, and J. Lee. 2018. Bending and free vibration analyses of in-plane bi-directional functionally graded plates with variable thickness using isogeometric analysis. Composite Structures 192:434–51. doi:10.1016/j.compstruct.2018.03.021.
   Web of Science ®Google Scholar
• Liew, K. M., X. Zhao, and A. J. M. Ferreira. 2011. A review of meshless methods for laminated and functionally graded plates and shells. Composite Structures 93 (8):2031–41. doi:10.1016/j.compstruct.2011.02.018.
   Web of Science ®Google Scholar
• Lim, T.-C. 2016. Higher-order shear deformation of very thick simply supported equilateral triangular plates under uniform load. Mechanics Based Design of Structures and Machines 44 (4):514–22. doi:10.1080/15397734.2015.1124784.
   Web of Science ®Google Scholar
• Liu, D. Y., C. Y. Wang, and W. Q. Chen. 2010. Free vibration of FGM plates with in-plane material inhomogeneity. Composite Structures 92 (5):1047–51. doi:10.1016/j.compstruct.2009.10.001.
   Web of Science ®Google Scholar
• Love, A. E. H. 1888. The small free vibrations and deformation of a thin elastic shell. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 179:491–546. doi:10.1098/rsta.1888.0016.
   Google Scholar
• Ma, L. S., and T. J. Wang. 2004. Relationship between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory. International Journal of Solids and Structures 41 (1):85–101. doi:10.1016/j.ijsolstr.2003.09.008.
   Web of Science ®Google Scholar
• Menasria, A., A. Kaci, and A. A. Bousahla. 2020. A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions. Steel and Composite Structures 36 (3):355–67. doi:10.12989/scs.2020.36.3.355.
   Web of Science ®Google Scholar
• Mindlin, R. D. 1951. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. Journal of Applied Mechanics 18:31–8.
   Web of Science ®Google Scholar
• Mohammadi, M., A. Saidi, and E. Jomehzadeh. 2010. Levy solution for buckling analysis of functionally graded rectangular plates. Applied Composite Materials 17 (2):81–93. doi:10.1007/s10443-009-9100-z.
   Web of Science ®Google Scholar
• Neves, A. M. A., A. J. M. Ferreira, E. Carrera, M. Cinefra, R. M. N. Jorge, and C. M. M. Soares. 2012. Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering zig-zag and warping effects. Advances in Engineering Software 52:30–43. doi:10.1016/j.advengsoft.2012.05.005.
   Web of Science ®Google Scholar
• Neves, A. M. A., A. J. M. Ferreira, E. Carrera, M. Cinefra, C. M. C. Roque, R. M. N. Jorge, and C. M. M. Soares. 2013. Static free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique. Composites Part B: Engineering 44 (1):657–74. doi:10.1016/j.compositesb.2012.01.089.
   Web of Science ®Google Scholar
• Rahmani, M. C., A. Kaci, A. A. Bousahla, F. Bourada, A. Tounsi, and E. A. A. Bedia. 2020. Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory. Computers and Concrete 25 (3):225–44. doi:10.12989/CAC.2020.25.3.225.
   Web of Science ®Google Scholar
• Reddy, J. N. 1984. A simple higher-order theory for laminated composite plates. Journal of Applied Mechanics 51 (4):745–52. doi:10.1115/1.3167719.
   Web of Science ®Google Scholar
• Reddy, J. N., C. M. Wang, and S. Kitipornchai. 1999. Axisymmetric bending of functionally graded circular and annular plates. European Journal of Mechanics: A/Solids 18 (2):185–99. doi:10.1016/S0997-7538(99)80011-4.
   Web of Science ®Google Scholar
• Reddy, J. N. 2000. Analysis of functionally graded plates. International Journal for Numerical Methods in Engineering 47 (1–3):663–84. doi:10.1002/(SICI)1097-0207(20000110/30)47:1/3 < 663::AID-NME787 > 3.0.CO;2-8.
   Web of Science ®Google Scholar
• Reissner, E. 1945. The effect of transverse shear deformation on the bending of elastic plates. Journal of Applied Mechanics 12:69–7.
   Web of Science ®Google Scholar
• Saidi, A. R., A. Rasouli, and S. Sahraee. 2009. Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory. Composite Structures 89 (1):110–9. doi:10.1016/j.compstruct.2008.07.003.
   Web of Science ®Google Scholar
• Senthilnathan, N. R., S. P. Lim, K. H. Lee, and S. T. Chow. 1987. Buckling of shear-deformable plates. Journals: The American Institute of Aeronautics and Astronautics: AIAA 25 (9):1268–71. doi:10.2514/3.48742.
   Google Scholar
• Soldatos, K. P. 1992. A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mechanica 94 (3–4):195–220. doi:10.1007/BF01176650.
   Web of Science ®Google Scholar
• Shi, G. 2007. A new simple third-order shear deformation theory of plates. International Journal of Solids and Structures 44 (13):4399–417. doi:10.1016/j.ijsolstr.2006.11.03.
   Web of Science ®Google Scholar
• Timoshenko, S. P., and S. Woinowsky-Kriger. 1959. Theory of plates and shells. New York: McGraw-Hill.
   Google Scholar
• Thai, C. H., N. V. D. Vuong, and H. Nguyen-Xuan. 2016. An improved moving kriging-based meshfree method for static, dynamic and buckling analyses of functionally graded isotropic and sandwich plates. Engineering Analysis with Boundary Elements 64:122–36. doi:10.1016/j.enganabound.2015.12.003.
   Web of Science ®Google Scholar
• Touratier, M. 1991. An efficient standard plate theory. International Journal of Engineering Science 29 (8):901–16. doi:10.1016/0020-7225(91)90165-Y.
   Web of Science ®Google Scholar
• Tran, L. V., A. J. M. Ferreira, and H. Nguyen-Xuan. 2013. Isogeometric analysis of functionally graded plates using higher-order shear deformation theory. Composites Part B: Engineering 51:368–83. doi:10.1016/j.compositesb.2013.02.045.
   Web of Science ®Google Scholar
• Vu, T. V., J. L. Curiel-Sosa, and T. Q. Bui. 2018b. A refined sin hyperbolic shear deformation theory for sandwich FG plates by enhanced meshfree with new correlation function. International Journal of Mechanics and Materials in Design 15 (3):647–69. doi:10.1007/s10999-018-9430-9.
   Web of Science ®Google Scholar
• Vu, T. V., A. Khosravifard, M. R. Hematiyan, and T. Q. Bui. 2018a. A new refined simple TSDT-based effective meshfree method for analysis of through-thickness FG plates. Applied Mathematical Modelling 57:514–34. doi:10.1016/j.apm.2018.01.004.
   Web of Science ®Google Scholar
• Vu, T. V., A. Khosravifard, M. R. Hematiyan, and T. Q. Bui. 2018c. Enhanced meshfree method with new correlation functions for functionally graded plates using a refined inverse sin shear deformation plate theory. European Journal of Mechanics: A/Solids 74:160–75. doi:10.1016/j.euromechsol.2018.11.005.
   Web of Science ®Google Scholar
• Vu, T.-V., N.-H. Nguyen, A. Khosravifard, M. R. Hematiyan, S. Tanaka, and T. Q. Bui. 2017. A simple FSDT-based meshfree method for analysis of functionally graded plates. Engineering Analysis with Boundary Elements 79:1–12. doi:10.1016/j.enganabound.2017.03.002.
   Web of Science ®Google Scholar
• Vu, T. V., and V. S. Phan. 2017. A modified moving kriging interpolation-based meshfree method with refined sinusoidal shear deformation theory for analysis of functionally graded plates. In ACOME 2017: Proceedings of the International Conference on Advances in Computational Mechanics 2017, ed. H. Nguyen-Xuan, P. Phung-Van, and T. Rabczuk, 485–501. Singapore: Springer. doi:10.1007/978-981-10-7149-2_33.
   Google Scholar
• Yin, S. H., T. T. Yu, and P. Liu. 2013. Free vibration analyses of FGM thin plates by isogeometric analysis based on classical plate theory and physical neutral surface. Advances in Mechanical Engineering 5. doi:10.1155/2013/:634584.
   Google Scholar
• Yin, S., J. S. Hale, T. Yu, T. Q. Bui, and S. P. A. Bordas. 2014. Isogeometric locking-free plate element: A simple first order shear deformation theory for functionally graded plates. Composite Structures 118:121–38. doi:10.1016/j.compstruct.2014.07.028.
   Web of Science ®Google Scholar
• Zenkour, A. M. A. 2005. A comprehensive analysis of functionally graded sandwich plates: Part 2: Buckling and free vibration. International Journal of Solids and Structures 42 (18–19):5243–58. doi:10.1016/j.ijsolstr.2005.02.016.
   Web of Science ®Google Scholar