This study presents the development of the partial hybrid finite element method for the stress analysis of laminated composite structures. The authors hold that the partial hybrid finite element method is more efficient than the displacement-based finite element method for the stress analysis of laminated composites. Since there is a great need for accurate and efficient calculation of interlaminar stresses for designs using composites, the partial hybrid finite method does provide one possible solution. This work is the culmination of the work of three generations of PhD students in the Concordia Centre for Composites. Particular points of interest include: a new ISO function method and classification of stress modes which allow the systematic determination of stress polynomials; how the hybrid finite elements and global/local approach allow the stress analysis of laminated composites to be five times more efficient than the displacement finite element method; a detailed description of three different types of hybrid finite elements for laminated composites.This study should be of interest to researchers and designers of laminated composites as well as finite element method students and programmers of finite element codes.
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.