Buckling Analysis of Functionally Graded Sandwich Beam Based on Third-Order Zigzag Theory

In this paper buckling response of a sandwich (SW) beam containing functionally graded skins and metal (Type-S) or ceramic core (Type-H) is investigated using a third-order zigzag theory. The variation of material properties in functionally graded (FG) layers is quantified through exponential and power laws. The displacements are assumed using higher-order terms along with the zigzag factors to evaluate the effect of shear deformation. In-plane loads are considered. The governing equations are derived using the principle of virtual work. The model achieves stress-free boundaries unlike higher-order shear deformation theories and is C۰ continuous so, does not require any post-processing method. The present model shows an accurate variation of transverse stresses in thickness direction due to the inclusion zigzag factor in assumed displacements and is independent of the number of layers in computing the results. Numerical solutions are arrived at by using three noded finite elements with ۷DOF/node for sandwich beams. The novelty of the paper lies in presenting a zig-zag buckling analysis for the FGSW beam with thickness stretching. This paper presents the effects of the power law factor, end conditions, aspect ratio, and lamination schemes on the buckling response of FGM sandwich beams. The numerical results are found to be in accordance with the existing results. The buckling strength was improved by increasing the power law factor for Type S beams while the opposite behavior was seen in type H beams for all types of end conditions. The end conditions played a major role in deciding the buckling response of FGSW beams. Exponential law governed FGSW beam exhibited a little higher buckling resistance for Type S beams, while a little lower buckling resistance was found for Type S beams for almost all lamination schemes and end conditions. Some new results are also presented which will serve as a benchmark for future research in a parallel direction.

Keywords:

Buckling Analysis , Zigzag theory , Power law , Exponential law , Functionally Graded Material