Buckling Analysis of Functionally Graded Material Plates Using Higher Order Shear Deformation Theory

Abstract

The prime aim of the present study is to present analytical formulations and solutions for the buckling analysis of simply supported functionally graded plates (FGPs) using higher order shear deformation theory (HSDT) without enforcing zero transverse shear stresses on the top and bottom surfaces of the plate. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. Material properties of the plate are assumed to vary in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. The equations of motion and boundary conditions are derived using the principle of virtual work. Solutions are obtained for FGPs in closed-form using Navier’s technique. Comparison studies are performed to verify the validity of the present results from which it can be concluded that the proposed theory is accurate and efficient in predicting the buckling behavior of functionally graded plates. The effect of side-to-thickness ratio, aspect ratio, modulus ratio, the volume fraction exponent, and the loading conditions on the critical buckling load of FGPs is also investigated and discussed.

Experimental Research and Method for Calculation of 'Upsetting-with-Buckling' Load at the Impression-Free (Dieless) Preforming of Workpiece

“…The results of studies [12] show that the use of workpieces with a profiled lateral surface allows to increase the value of the critical load by 20...40% in comparison with not preformed workpieces. An important factor is the shape factor, namely the effect of "side-to-thickness ratio" and for functionally structured materials for support plates production, to which specific requirements are imposed [13].…”

Mechanical Buckling Analysis of Functionally Graded Plates Using an Accurate Shear Deformation Theory

“…Karama et al were interested in the mechanical behavior of laminated composite beams by the new model of multilayer laminated composite structures with continuity of transverse shear stresses [27]. B. Sidda Reddy et al to use the theory of high order shear deformation to analyze the buckling of functionally graduated material plates [28]. Otherwise, the simple refined theory is used for the analysis of buckling of plates with functional gradation by [29].…”

Nonlinear vibration analysis of piezolaminated functionally graded cylindrical shell

“…The buckling solution is obtained using the Ritz method with Chevyshev polynomials as assumed displacement functions. The vibration behaviour of FG plate is studied by Reddy et al (2014) analytically using higher order shear deformation theory. Principle of virtual work is used to derive equation of motion and solution is obtained in closed form using Navier's technique.…”