Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion

In this paper, the buckling problem of thin rectangular functionally graded plates subjected to proportional biaxial compressive loadings with arbitrary edge supports is investigated. Classical plate theory (CPT) based on the physical neutral plane is applied to derive the stability equations. Mechanical properties of the FGM plate are assumed to vary continuously along its thickness according to a power law function. The displacement function is considered to be in the form of a double Fourier series whose derivatives are determined using Stokes' transformation. The advantage of this method is capability of considering any possible combination of boundary conditions with no necessity to be satisfied in the Fourier series. To give generality to the problem, the plate is assumed to be elastically restrained by means of rotational and translational springs at the four edges. Numerical examples are presented, and the effects of the plate aspect ratio, the FGM power index, and the loading proportionality factor on the buckling load of an FGM plate with different usual boundary conditions are studied. The present results are compared with those have been previously reported by other analytical and numerical methods, and very good agreement is seen between the findings indicating validity and accuracy of the proposed approach in the buckling analysis of FGM plates.

► We studied the buckling of thin rectangular FGM plates with arbitrary edge supports.
► Classical plate theory (CPT) based on the physical neutral plane was applied.
► We exploited Fourier series as displacement function and using Stokes' transformation.
► The buckling load increases by more constraining of the plate edges.
► The present method can be extended to buckling as well as vibration analysis of beams and shells.