Thermo-mechanical buckling analysis of thick beams reinforced with agglomerated CNTs with temperature-dependent thermo-mechanical properties under a nonuniform thermal loading

In this article, the thermo-mechanical buckling analysis of composite beams reinforced with carbon nanotubes (CNTs) subjected to a nonuniform thermal loading is studied. To increase the accuracy of results, the beam is modeled based on the quasi-3D sinusoidal shear deformation beam theory which considers shear deformation and thickness stretching. Temperature-dependent thermo-mechanical properties care considered for both polymeric matrix and CNTs. The CNTs are orientated randomly and distributed along thickness direction based on various symmetric and nonsymmetric patterns and agglomeration of CNTs is incorporated. The heat conduction equation is solved analytically to obtain the temperature profile along the thickness direction. The governing equations and associated boundary conditions regarding the thermo-mechanical analysis of the beam are derived using Hamilton's principle and solved numerically using the differential quadrature method. Convergence and accuracy of the presented solution are confirmed, and the influences of various parameters on the thermo-mechanical stability regions are investigated, such as boundary conditions, thickness-to-length ratio, mass fraction and distribution pattern of the CNTs, and the CNTs agglomeration parameters. Numerical results reveal that to achieve the most expanded thermo-mechanical stability regions, it is more helpful to distribute the CNTs as far as away from the middle axis of the beam, especially near the surface with lower temperature. It is observed that neglecting the temperature-dependency of thermo-mechanical properties results in an overestimate of the critical temperature, and this overestimate is more noticeable for the beams with more constrained boundary conditions.