Modeling and predicting the response and failure of laminated composite structures is a very challenging task. On one hand the designer is interested in the overall response of the structure, but on the other he is also interested in modeling phenomena such as damage which have a localized behavior. The ideal solution would be to carry out the analysis at a global level enhancing the model by adding localized information when needed.
Plate models dimensionally reduce a finite element method (FEM) problem by imposing constraints on the through thickness variation of the displacement field. In this work, the displacement field is represented as the superposition of a number of plate fields, and a unifying strain field is derived. By appropriately defining boundaries to the ‘enhancing’ displacement fields, it is demonstrated that the superposition of displacement fields can be used to locally enrich the solution where more information is required. In this manner, an efficient global model can be used to determine gross displacements, and an enriching model can be used to determine stresses at lamina interfaces for the accurate prediction of localized phenomena. The proposed theoretical framework would allow an analyst to study both thin and thick walled laminated structures by introducing simple switch-over criteria between single and multiple layer theories.
The model is implemented using an extended FEM (X-FEM) and superposition approach. Extra degrees of freedom are added to the model to represent the additional displacement fields, and the meshing process remains independent for each field. Both equivalent single layer theories and discrete layer theories are incorporated into the general unified framework. Geometric nonlinearities are also included in the form of the von Kármán equations. Delaminations are integrated by performing an extrinsic enrichment of the assumed displacement fields. A cohesive law between laminae was also incorporated to calculate the tensile and shear tractions.
The present paper outlines the various general theories to describe in-plane and out-plane displacements fields, then a unified theoretical framework is formulated and finally the finite element formulation which is based on a multilevel mesh superposition approach is reported.