Pseudo-spectral method for mechanical buckling analysis of circular plates with variable thickness made of bimorph FGMs

Document Type : Research


1 Assistant Professor, Department of Civil Engineering, Hakim Sabzevari University, Sabzevar, Iran

2 Ph.D. Student, Department of Mechanical Engineering, Faculty of Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran.

3 Associate Professor, Department of Civil Engineering, Hakim Sabzevari University, Sabzevar, Iran


In this paper, the mechanical buckling behavior of circular plates with variable thicknesses made of bimorph functionally graded materials (FGMs) under uniform mechanical loading circumstances has been studied for the first time. The governing equations are derived based on the first-order shear deformation plate theory and von Karman's assumptions. The material characteristics are symmetric about the middle plane of the plate and these characteristics vary along the thickness direction according to the power law. The middle plane of the plate is made of pure metal, which changes to pure ceramic as it approaches the outer sides. In order to determine the pre-buckling force in the radial direction, the membrane equation is solved using the shooting method. Then, the stability equations are solved numerically with the help of pseudo-spectral method and choosing the Chebyshev polynomials as basis functions. The numerical results are presented for both clamped and simply supported boundary conditions by considering linear and parabolic patterns for the thickness variations. The influences of various parameters like volume fraction index, thickness profile and side ratio on the buckling behavior of these plates have been evaluated. The obtained numerical results show that there exists an optimal value for the thickness parameter, wherein the buckling load becomes maximum. The buckling load of circular FGM plates increases more than 100% when the volume fraction index increases from 0 to 5. The buckling load of the clamped circular FGM plates decreases about 15% as the side ratio increases from 0.01 to 0.2.  


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