Analysis of circular free edge effect in composite laminates by p-convergent global–local model

In this paper the p-convergent global–local model based on layerwise theory is presented to predict the complicated patterns of stress fields around a circular hole of composite laminates under tension. A distinction of this model is to combine two-dimensional elements with three-dimensional elements in a designed mesh. In the local region with high stress gradient, three-dimensional displacement fields can be defined by layer-by-layer representation, while equivalent single-layer elements are adopted in the global region with smooth stress gradient. Also, the p-refinement in local as well as global regions is simultaneously implemented using Lobatto shape functions. Higher-order shape functions for three-dimensional elements are derived by the combination of one- and two-dimensional shape functions in a layerwise sense. In this study the orders of the shape functions are kept to be fixed as p-level (in-plane direction)=8 and q-level (thickness direction)=5 from the convergence test of in-plane and transverse stresses. The proposed model achieves compatibility displacements and stress equilibrium at the junction or interface between the different element types. Also, exact mapping of curved boundary is undertaken using blending functions. Numerical examples of curved free-edge problems have been taken into account to illustrate the performance of the present approach. Numerical results show that the proposed model is capable of predicting in-plane stresses around a circular hole as well as interlaminar stresses at the interface between layers.