Development of partial hybrid finite elements for 3-D global/local analysis of laminated composite structures

The purpose of this work is to develop global/local finite element models using partial hybrid stress finite elements for stress analysis of laminated composite structures. Based on the composite variational principle, the general formulations of partial hybrid single-layer finite element and multilayer finite element are presented. These formulations can be used to develop a series of partial hybrid finite elements. A 4-node degenerated plate element, an 8-node degenerated plate element, a 3-D, 8-node solid element, a 3-D, 20-node solid element, a 6-node transition element, a 15-node transition element, a multilayer solid element, and a multilayer transition element are presented. The elements developed in this thesis are examined by the, eigenvalue test to detect zero-energy deformation modes and the absence of rigid-body motion capability. The results show that the elements do not have any kinematic deformation modes, and they have a desired capability for rigid-body displacement. In addition, the non-zero eigenvalues of the element stiffness matrices are real and positive. In order to determine the optimal partial stress fields for the partial hybrid elements, a classification method of stress modes is presented. The method can be used to classify stress modes, select optimal stress modes, and set up an assumed stress matrix for a hybrid element. Also, the necessary and sufficient condition for avoiding spurious kinematic deformation mode is proposed and the optimal condition of an assumed stress field is presented. A computer program COMSA is developed to implement the partial hybrid finite element method. The Global/Local finite element models are established using plate element, solid element, and transition element. In the thesis, a few numerical examples are presented to verify the accuracy and efficiency of the finite element models. It has been shown that the global/local models using partial hybrid element are efficient and accurate for stress analysis of laminated composites due to the fact that they take advantage of the capacity of both 3-D elements and 2-D elements