Keywords: functionally graded material, thermal buckling, axisymmetric, circular plate, unconstrained third-order plate theory.

In this paper, axisymmetric thermal buckling of functionally graded circular plates (FGCPs) is considered using unconstrained third-order shear deformation plate theory (UTST). The UTST releases the shear-free condition on the top and bottom surfaces of the plate in order to comprise the presence of shear stress parallel to plate. This theory can be particularly useful when the plate is subjected to contact friction or presented in a flow field where the boundary layer shear stress is not infinitesimally small. Since the UTST represents a quadratic variation of the transverse shear stress through the thickness of plate, unlike the first order shear deformation plate theory (FST), it does not require the shear correction factor. The UTST with one additional unknown function in comparison with the Reddy's third-order shear deformation theory (TST) has the governing differential equation of the same order (for the axisymmetric analysis of circular plates) [1]. This is because the UTST has more practical equilibrium equations. Also, it is more adoptable as it can be degenerated to first- and third-order plate theories straightforwardly.

In this research, equilibrium and stability equations of FGCPs are generally derived in polar coordinates through a variational approach. Then, using the axisymmetric conditions, the resulting equations are reduced to the case of completely functionally graded material (FGM) circular plates. Using an analytical method, the solutions for critical buckling temperature of a FGCP subjected to two types of thermal loadings, namely; uniform temperature rise and a graded temperature rise through the thickness are presented. It is seen that the higher-order plate theories underestimate the buckling temperature in comparison with the FST solutions. Also, it is observed that the UTST results are virtually the same as to those obtained using the TST from which can be concluded that the effect of vanishing transverse shear stress is not considerable and thus, the TST results are satisfactorily reliable.

1

M.M. Najafizadeh, H.R. Heydari, "Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory", European journal of Mech. A/Solids, 23, 1085-1100, 2004. doi:10.1016/j.euromechsol.2004.08.004

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