Two-noded zigzag beam element accounting for shear effects based on an extended Euler Bernoulli theory

Published in Composite Structures, Vol. 132, pp 1192-1205, 2015
DOI: 10.1016/j.compstruct.2015.07.031

Abstract

We present a new 2-noded beam element based on the refined zigzag theory and the classical Euler–Bernoulli beam theory for the static analysis of composite laminate and sandwich beams. The proposed element is able to take into account distortion effects due to shear elastic strains and can predict delamination. The element has four degrees of freedom per node. A $C^{1}$ cubic Hermite interpolation is used for the vertical deflection while a $C^{0}$ linear interpolation is employed for the other kinematics variables. The stiffness matrix and the load vector are calculated in explicit form using exact integration. The element is free from shear locking as confirmed with numerical tests on a wide range of the slenderness ratios. Numerical results show the ability of the EEBZ2 element to reproduce accurately the vertical deflection along the beam length and complex zigzag distributions of the axial displacement and the stresses across the thickness. Delamination effects are modeled by incorporating of an additional zigzag function corresponding to the kinematics of a zero thickness layer where delamination occurs. An example showing the capability of the new EEBZ2 element for accurately reproducing delamination effects is presented.