Combining X-FEM and a multilevel mesh superposition method for the analysis of thick composite structures

The use of simultaneous multiple plate models offers an attractive and alternative solution to full scale three-dimensional finite element method for the global-local analysis of laminated composite structures. In this paper, an approach is proposed where the less accurate plate model, used to carry out the analysis at the global level, is enhanced by more accurate and complex plate models in each laminate subregion where more accurate transverse stress or strain estimation is required (the local level). The total displacement is represented as the superposition of the displacements of a number of plate models. By appropriately defining boundaries to the enhancing model/region, it is demonstrated that the superposition of displacements can be used to locally enrich the solution where accurate through-the-thickness stresses are required. In this manner, a computationally efficient global model can be used to determine gross displacements, and potentially the enriched models can be used to determine stresses at lamina interfaces for the accurate prediction of localized phenomena such as damage initiation and growth. The model is implemented combining an extended FEM (X-FEM) and multilevel mesh superposition approach (MMSA). Extra degrees-of-freedom are added to the model to represent the additional displacement fields, and the meshing process remains independent for each field. The displacements and stresses computed by this approach are compared to literature data and analytical solutions for various plate geometries and loads showing an excellent correlation. Morevoer, the results showed, as expected, that the accuracy of the approximation is improved by the proposed approach compared to using the global plate model alone.