Enhancing buckling analysis of functionally graded plates using unified and generalized higher-order shear deformation theories

Abstract

This paper introduces a comprehensive framework for stability analysis of functionally graded plates under diverse in-plane loading conditions while employing higher-order shear deformation theories. For this purpose, a unified model, including all shear deformation kinematics, has been proposed. This unified model incorporates any number or type of shear transverse functions, encompassing all existing plate shear deformation theories. This inclusivity is achieved through the introduction of a unique parameter, denoted by ”n” representing the number of shear deformation functions in the displacement model. Such a unified model allows great flexibility in choosing among higher order theories when modeling the behavior of plates subjected to shear deformation, making it a valuable tool for applications in engineering and materials science. Besides, this allowed us to easily introduce a fifth-order theory used for the first time in the buckling analysis of FGM plates. The critical buckling loads expressions corresponding to the employed kinematics were derived and the calculated values are compared to those computed using the numerical solver. The comparison demonstrates the effectiveness and accuracy of the formulated expressions in predicting critical buckling loads under uniaxial and biaxial loading conditions.