Closed form stability solution of simply supported anisotropic laminated composite plates under axial compression compared with experiments

Abstract

Closed form expression for the buckling load of generally anisotropic laminated composite simply supported thin plates is derived. The Rayleigh-Ritz displacement field approximation based on the energy approach introduced an upper bound solution compared to the FE results. Therefore, the critical stability matrix is used to obtain an accurate buckling formula. The effective axial, coupling and flexural stiffness coefficients of the anisotropic layup is determined from the generalized constitutive relationship using dimensional reduction by static condensation of the 6×6 composite stiffness matrix. The resulting explicit formula has an additional term, which is a function of the effective coupling and axial stiffness. This formula reduces down to Euler buckling formula once the effective coupling stiffness term vanishes for isotropic and certain classes of laminated composites. The closed form results are verified against finite element Eigenvalue solutions for a wide range of anisotropic laminated layups yielding high accuracy. Comparisons with a limited number of experiments are also performed showing good correspondence. A brief parametric study is then conducted to examine the effect of ply orientations and material properties including hybrid carbon/glass fiber composites. Relevance of the numerical and closed form results is discussed for all these cases.