Analytical and finite element buckling solutions of fixed-fixed anisotropic laminated composite wide plates under axial compression

Using Rayleigh-Ritz approximation, a generalized analytical buckling formula was developed of generally anisotropic laminated fixed-fixed composite plates. Using the generalized constitutive equation, the effective extensional, coupling, and flexural stiffness coefficients of the anisotropic layup are determined using dimensional reduction by static condensation of 6x6 composite stiffness matrix. The resulting explicit formula is expressed in terms of the flexural stiffness coefficients as well as the plate geometry. In order to decrease some of the discrepancy in some of the results, the coupling and extensional effect was considered through the substitution of the pre-buckling solution into the bifurcation expression to yield a new formula. The analytical results are verified against finite element Eigen value solutions for a wide range of anisotropic laminated layups yielding high accuracy. A parametric study is then conducted to examine the effect of ply orientations, material properties and type of element in FE analysis. Relevance of the numerical and analytical results is discussed for all these cases.