Buckling behavior of composite and functionally graded material plates

In this work the formulation for linear buckling and for geometrically nonlinear analysis of laminated composite and functionally graded material (FGM) plates under mechanical uniaxial in-plane uniform loads, and thermal loads, is presented. An implemented finite element model based on a non-conforming triangular flat plate/shell element with three nodes and eight degrees of freedom per node, associated with a higher order shear deformation theory is used. The through the thickness variation of the material properties, discrete for laminated composite plates or continuous for FGM plates, as well as the through the thickness temperature distribution, originate a nonsymmetry with respect to the middle-surface. Thus, in general, the occurrence of bifurcation-type buckling should be studied, and the transverse deflection at the centre of the plate could be a good indicator to anticipate this occurrence. The solutions of some illustrative examples involving different boundary conditions, composite lay-up, FGM variation of volume fractions, temperature distributions, material combinations, and boundary conditions are presented for benchmarking purposes, with emphasis for the plate transverse deflections. Linear solutions are compared with numerical alternative models. The occurrence of bifurcation-type buckling is discussed for several representative cases, the validity of the linear buckling solutions is addressed and nonlinear analyses have been performed for confirmation purposes.