Nonlinear bending of thin and thick unsymmetrically laminated composite beams using refined finite element model

Abstract

Nonlinear bending behaviour of unsymmetrically laminated composite beams using von Karman's large deflection theory is investigated. For this purpose, a one-dimensional finite element having twelve degrees of freedom per node based on a simple higher shear deformation theory (HSDT) which satisfies the zero transverse shear stress at the top and bottom surface and avoids the use of shear correction factors is developed. The advantage of the present higher order theory is that first-order shear deformation theory (FSDT) and classical lamination theory (CLT) can be obtained easily by dropping the higher order terms associated with transverse shear deflection or all the terms associated with transverse shear deflection from the kinematic relations. To show the effect of transverse shear on the transverse deflection, the first-order shear deformation theory and classical lamination theory results are also presented. Unsymmetrically laminated composite beams, due to the existence of bending-extension coupling are shown to have direction dependent nonlinear bending stiffness, resulting in softening/hardening type of nonlinearity for one direction of transverse loading and hardening type nonlinearity for the other direction. It is shown that this softening type of nonlinearity at small loads changes to hardening type of nonlinearity for higher loads. Results are presented for various types of lay-ups, slenderness ratios and boundary conditions.