Instability finite element analysis of fibre reinforced composite structures based on the third order theory

In this paper a refined higher-order shear deformation theory for the instability finite element analysis of fibre reinforced shell like composite structures is developed. A higher order shear deformation theory allows parabolic description of the transverse shear stresses and therefore the shear correction factors of the usual shear deformation theory are not required. The present formulation is based on a higher order shear theory in which in-plane displacements are expanded as cubic functions of the thickness coordinate. The conditions of zero transverse shear stresses on the top and bottom faces are satisfied. Laminate material is assumed to be linearly elastic, homogeneous and isotropic/orthotropic. The 4-node quadrilateral shell finite element with 8 degrees of freedom per node has been developed which eleviates most of the deficiencies associated with such types elements. The effects of the transverse shear deformation on the buckling loads are investigated. It is shown that the present theory predicts buckling loads more accurately then CTP or the first order shear deformation theory. To determine buckling loads here is used Lanczos algorithm. The good agreement of the numerical and experimental results is indicative of a reliable presented shell element and procedure for practical instability analysis of the structures made of the fiber reinforced laminates.