On buckling characteristics of polymer composite plates reinforced with graphene platelets


In the present study, buckling analysis of polymer composite plates reinforced with graphene platelets (GPLs) in thermal environment is investigated based on higher-order shear deformation plate theory. Halpin–Tsai model is used to determine the material properties of multilayer polymer composite plate. In the present study, four patterns of GPL distribution in composite plate are considered. To obtain the Euler–Lagrange equations of composites plate, Hamilton’s principle is employed and utilized Navier’s method for analyzing and solving the problem. The results of this study have been verified by checking them with the previous works. The effects of various parameters such as geometry effect, GPL weight fraction and temperature changes on critical buckling temperature are explored.

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Correspondence to Farzad Ebrahimi or Ali Toghroli.

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$$\begin{aligned} K_{11} & = - m^{2} A_{11} - n^{2} \left( {A_{44} } \right) \\ K_{12} & = - mnA_{12} - mnA_{44} \\ K_{13} & = c_{1} m^{3} \left( {D_{11} } \right) + c_{1} n^{2} m\left( {D_{12} } \right) + 2c_{1} mn^{2} \left( {D_{44} } \right) \\ K_{14} & = - m^{2} \left( {B_{11} } \right) + c_{1} m^{2} \left( {D_{11} } \right) + c_{1} n^{2} \left( {D_{44} } \right) - n^{2} B_{44} \\ K_{15} & = mnc_{1} D_{12} - mnB_{44} + mnc_{1} D_{44} - mnB_{12} \\ K_{21} & = K_{12} \\ K_{22} & = - n^{2} A_{22} - m^{2} A_{44} \\ K_{23} & = c_{1} n^{3} D_{22} + mn^{2} c_{1} D_{12} + 2m^{2} nc_{1} D_{44} \\ K_{24} & = - mnB_{12} + c_{1} mnD_{12} - mnB_{44} c_{1} mnD_{44} \\ K_{25} & = - n^{2} B_{22} + c_{1} n^{2} D_{22} - m^{2} B_{44} + C_{1} m^{2} B_{44} \\ K_{31} & = K_{13} \\ K_{32} & = K_{23} \\ K_{33} & = - m^{4} c_{1}^{2} G_{12} + n^{2} m^{2} \left( { - 2c_{1}^{2} G_{12} - 4c_{1}^{2} G_{44} } \right) - n^{4} c_{1}^{2} G_{22} \\ & \quad - m^{2} \left( {A_{55} - 6c_{1} C_{55} + 9c_{1}^{2} E_{55} } \right) - n^{2} \left( {A_{66} - 6c_{1} C_{66} + 9c_{1}^{2} E_{66} } \right) \\ K_{34} & = c_{1} m^{3} E_{11} - c_{1}^{2} m^{3} G_{11} + mn^{2} \left( {c_{1} E_{12} - c_{1}^{2} G_{12} + 2c_{1} E_{44} - 2c_{1}^{2} G_{44} } \right) \\ & \quad - 3c_{1} mA_{55} C_{55} + 3c_{1} m\left( {C_{55} - 3c_{1} E_{55} } \right) \\ K_{35} & = m^{2} n\left( { - c_{1}^{2} G_{12} + 2c_{1} E_{44} - 2c_{1}^{2} G_{44} + c_{1} E_{12} } \right) - n^{3} c_{1}^{2} G_{22} \\ & \quad - 3c_{1} nA_{66} C_{66} + 3c_{1} n\left( {C_{66} - 3c_{1} E_{66} } \right) + c_{1} n^{3} E_{22} \\ K_{41} & = K_{14} \\ K_{42} & = K_{24} \\ K_{43} & = K_{34} \\ K_{44} & = - m^{2} \left( {C_{11} - 2c_{1} E_{11} + c_{1}^{2} G_{11} } \right) - n^{2} (C_{44} - 2c_{1} E_{44} + c_{1}^{2} G_{44} + 3c_{1} \left( {C_{55} - 3c_{1} E_{55} } \right) - 3c_{1} A_{55} C_{55} \\ K_{45} & = - mn(c_{1} E_{12} + C_{44} - c_{1} E_{44} + c_{1}^{2} G_{12} - c_{1} E_{44} + c_{1}^{2} G_{44} + C_{12} - c_{1} E_{12} \\ K_{51} & = K_{15} \\ K_{52} & = K_{25} \\ K_{53} & = K_{35} \\ K_{54} & = K_{45} \\ K_{55} & = - n^{2} \left( {C_{22} - 2c_{1} E_{22} + c_{1}^{2} G_{22} } \right) - m^{2} \left( {C_{44} - 2c_{1} E_{44} c_{1}^{2} G_{44} } \right) + 3c_{1} C_{66} - A_{66} + 3c_{1} \left( {C_{66} - 3c_{1} E_{66} } \right) \\ \end{aligned}$$

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Shariati, A., Qaderi, S., Ebrahimi, F. et al. On buckling characteristics of polymer composite plates reinforced with graphene platelets. Engineering with Computers (2020). https://doi.org/10.1007/s00366-020-00992-2

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  • Buckling
  • GPLRC plate
  • Thermal environment
  • Higher-order shear deformation beam theory