Nonlinear thermal buckling analyses of functionally graded circular plates using higher-order shear deformation theory with a new transverse shear function and an enhanced mesh-free method

Abstract

This study presents nonlinear buckling analyses of functionally graded (FG) circular plates in thermal environments using a mesh-free method. The thermal buckling response is formulated based on higher-order shear deformation plate theory in which a new transverse shear function is incorporated to better represent the displacement fields. An enhanced mesh-free radial point interpolation method (RPIM) in which the shape functions are constructed without any fitting parameters by virtue of the radial basis function in a compactly supported form is developed and utilized to explore the thermal buckling behavior. A radial basis function in a compactly supported form is proposed and included in the RPIM. Two types of FG circular plates with different FGM orientation, i.e., metal–ceramic FG circular plates and ceramic–metal FG circular plates, are considered in the analyses. The effectiveness and accuracy of the enhanced RPIM based on the higher-order shear deformation theory is first confirmed by simulating a numerical example found in the literature and comparing the results with the analytical solutions. Detailed parametric studies are then performed to investigate the effects of the volume fraction, plate thickness-to-radius ratio and metallic surface temperature on the critical buckling temperatures of FG circular plates subjected to various through-thickness temperature distributions. Results demonstrate that the enhanced mesh-free RPIM based on the higher-order shear deformation plate theory with the proposed transverse shear function can effectively predict the thermal buckling responses of FG circular plates, and that the volume fraction, plate thickness-to-radius ratio, bottom surface temperature and FGM orientation have considerable effects on the critical buckling temperatures.