Development of Hybrid Element Technique for Analysis of Composites

Abstract

The previous two chapters presented a brief overview of the displacement finite element formulation and the hybrid finite element formulation. These finite element formulations have been used for the analysis of structures made of isotropic materials. They also have been used for the analysis of laminated composite structures. However, the results for laminated composite structures need improvement due to the fact that there are many levels of discontinuities in the laminated composites. These discontinuities give rise to many regions of high stress gradients. On the microstructural level, there is discontinuity in material properties as one moves from fiber to matrix or vice versa. For the purpose of calculation at the lamina level, the fiber and matrix properties are averaged over an effective unit cell and the effective modulus approach is used for macromechanics. The average properties of individual lamina are usually obtained based on this assumption. Moreover, when many laminae are stacked to form laminates, due to the variation in fiber orientation from lamina to lamina, the interlaminar stresses occur near the interfaces between the laminae. The interlaminar failure modes caused by the interlaminar stresses are major failure modes in laminates because interlaminar strengths are usually orders of magnitude smaller than intralaminar strengths. This problem has been with designers and researchers for the past thirty years. Many numerical techniques have been proposed, the majority of them using the finite element method [3.1]. However until the present time, the problem has not been resolved satisfactorily. The main difficulty is in the efficiency in obtaining transverse stresses accurately. Without efficient means to obtain accurate transverse stresses, it is difficult to obtain efficient ways to predict interlaminar failure.