Vibration and buckling analyses of functionally graded plates based on refined plate theory using airy stress function

Abstract

In this paper, an approach based on the refined plate theory and Airy stress function has been proposed to investigate the vibration and buckling behaviors of functionally graded (FG) rectangular plates. The significant feature of the proposed approach is considering only two unknowns in the displacement field in which the contribution due to shear and bending to the total transverse displacement are clarified. Using the extended Hamilton’s principle and defining an Airy stress function corresponding to the compatibility equation, the equations of motion, which do not explicitly include the in-plane displacements, are derived. The accuracy and effectiveness of the current model is shown by comparing the natural frequencies and buckling loads of various FG rectangular plates calculated by the proposed approach with even three-dimensional (3-D) and quasi-3D solutions. Besides, the exact dynamic response of a square FG plate due to a harmonic central force is investigated using modal analysis. This approach is capable of handling quasi-3D models , by selecting proper functions in the displacement field to consider the thickness stretching effect. By doing this, behavior of FG square plates with various coefficient functions are compared with each other. Therefore, through implementing the Airy stress function, the number of variables is reduced, in turn, simplifying the dynamic model. Consequently, it can be used for wide range study of static and dynamic behaviors of FG plates.

A Four-Variable Shear Deformation Theory for the Static Analysis of FG Sandwich Plates with Different Porosity Models

“…This numerical approach was built on hierarchical models derived from the accuracy of the spectrum model and the 2-D natural element method. Monajati et al [22] present a new RSPT-based approach for examining the vibration and buckling of FG plates. The Airy stress function excludes in-plane variables, resulting in only two state variables: transverse bending and transverse shear deformation.…”

Nonlinear buckling and post-buckling analyses of functionally graded circular shallow arches

“…When the literature is examined, it is seen that there is a large amount of papers on the static, stability and dynamic responses of FG beams, 28–44 plates and shells. 45–73 Curved beams or arches made of homogeneous materials are frequently encountered in various engineering applications. 74–82 However, studies on the structural analysis of the FG arches are limited.…”