Analytical and Finite Element Buckling Solutions of Fixed–Fixed Anisotropic Laminated Composite Columns Under Axial Compression

Abstract

A generalized analytical formula is developed to predict buckling of anisotropic laminated composite fixed–fixed thin columns by using the Rayleigh–Ritz displacement field approximation. Based on the generalized constitutive relationship, the effective extensional, coupling and flexural stiffness coefficients of the anisotropic layup are determined using dimensional reduction by static condensation of the 6[Formula: see text][Formula: see text][Formula: see text]6 composite stiffness matrix. The resulting explicit formula is expressed in terms of the flexural stiffness since the coupling and extensional stiffness coefficients drop out of the formulation for this boundary condition when following the standard Rayleigh–Ritz formulation steps. This formula is similar to the Euler buckling formula in which the flexural rigidity is expressed in terms of the flexural stiffness coefficient of laminated composites. Motivated by reducing some of the discrepancy with the finite element results, the pre-buckling solution was substituted into the bifurcation expression to yield an updated formula that includes the coupling and extensional stiffness coefficients. 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 orientation and material properties including hybrid carbon/glass fiber composites. Relevance of the numerical and analytical results is discussed for all these cases. In addition, comparisons with an earlier buckling solution for cross-ply laminated columns are made.