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In this article, a mathematical derivation is made to develop a nonlinear static model for the thermal post-buckling characteristics of an annular system reinforced with graphene nanoplatelets (GPLs) and coupled with the piezoelectric actuator (PA) and shape memory alloy (SMA) under lateral loading. The matrix material is reinforced with GPLs at the nanoscale. The displacement-strain of postbuckling analysis of the functionally graded-graphene nanoplatelets reinforced composite (FG-GPLRC) annular system via higher-order shear deformation theory (HSDT) and using Von Karman nonlinearity is obtained. The governing equations and boundary conditions are formulated via the minimum total potential energy principle, and they are solved with the generalized differential quadrature method (GDQM). The direct iterative approach is presented for solving the set of equations that include highly nonlinear parameters. Finally, the results show that SMA fiber, radius ratio of outer to the inner, geometrical parameter of GPLs, applied voltage, piezoelectric thickness, and large amplitude play an essential impact on the thermal postbuckling response of the annular sandwich system. Another important consequence is that the highest thermal postbuckling to thermal buckling ratio is for the GPL-O pattern for all ranges of the large amplitude while considering the GPL-X pattern leads to the lowest thermal postbuckling to thermal buckling ratio for the smart annular system. This study’s more general conclusion is that designing the FG-GPLRC annular system should be more attention to the nonlinearity parameter.

On instabilities and thermal post-buckling of the electrically annular system coupled with shape-memory alloy fibers