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.

1 Introduction.- 1.1 Introduction.- 1.2 Displacement finite element method.- 1.3 Assumed displacement field.- 1.4 Displacement element formulation.- 1.5 Advantages and disadvantages of displacement finite elements.- 1.6 Motivation for developing hybrid finite elements.- 2 The hybrid finite element method.- 2.1 Introduction.- 2.2 Formulation of the variational functional.- 2.3 Evolution of the hybrid finite element method.- 2.4 Assumed stress field.- 2.5 Difficulties with the hybrid finite element method.- 3 Development of hybrid element technique for analysis of composites.- 3.1 Introduction.- 3.2 Composite variational principle.- 3.3 Formulation of partial hybrid element.- 3.4 Determination of stress modes.- 4 Partial hybrid elements for analysis of composite laminates.- 4.1 Introduction.- 4.2 Single-layer finite elements.- 4.3 Multilayer finite elements.- 5 Numerical examples of finite element analysis and global/local approach.- 5.1 Introduction.- 5.2 Finite element analysis using degenerated plate element.- 5.3 Finite element analysis using solid element.- 5.4 Finite element analysis using multilayer element.- 5.5 Finite element models with different mesh densities.- 5.6 Global/local approach for stress analysis of composite laminates.- 5.7 Conclusion.