Development Of Partial Hybrid Finite Elements For 3 D Global Local Analysis Of Laminated Composite Structures

Hybrid Finite Element Method for Stress Analysis of Laminated Composites

This book has one single purpose: to present the development of the partial hybrid finite element method for the stress analysis of laminated composite structures. The reason for this presentation is because the authors believe that partial hybrid finite element method is more efficient that the displacement based finite element method for the stress analysis oflaminated composites. In fact, the examples in chapter 5 of this book show that the partial hybrid finite element method is about 5 times more efficient than the displacement based finite element method. Since there is a great need for accurate and efficient calculation of interlaminar stresses for the design using composites, the partial hybrid finite method does provide one possible solution. Hybrid finite method has been in existence since 1964 and a significant amount of work has been done on the topic. However, the authors are not aware of any systematic piece of literature that gives a detailed presentation of the method. Chapters of the displacement finite element method and the evolution 1 and 2 present a sununary of the hybrid finite element method. Hopefully, these two chapters can provide the readers with an appreciation for the difference between the displacement finite element method and the hybrid finite element. It also should prepare the readers for the introduction of partial hybrid finite element method presented in chapter 3.

Proceedings of the Tenth International Conference on Composite Materials

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.