Functionally refined model for cracked cylindrical shells repaired with laminated composite materials

This study is focused on the performance evaluation of composite laminated shells when the crack initiates and propagates longitudinally or circumferentially. For this purpose, two numerical composite shell models are considered. One is the equivalent single layer model, and the other is discrete-layer model. Both models are based on the p-convergent higher-order theory or called as the functionally refined model. The second model is mainly adopted and compared with the first model to predict the stress intensity factor in the vicinity of a crack tip not only before patch repair, but also after patch repair. The patch reinforcement effect has been analyzed with respect to various experimental parameters in terms of material type of patch, patch size, patch thickness, adhesive shear modulus, adhesive thickness, etc. The present model has a subprarmetric concept that considers linear mapping of geometry fields on a cylindrical coordinate, and hierarchical approximating functions are based on one- and two-dimensional integrals of Legendre polynomials, allowing accurate simulation of three-dimensional behavior. In assumed displacement field, stain-displacement relations and 3-D constitutive equations of one random layer are obtained by product of 1-D and 2-D higher-order shape functions. Thus it allows independent implementation of increasing p-level, order of shape function, for in-plane and out-of-plane displacement. In the proposed elements, the integrals of Legendre polynomials and Gauss-Lobatto technique are applied to interpolate displacement fields and to implement numerical integration. The sensitivity test has been carried out to show the robustness of present p-convergent higher-order element associated with severe element distortions, very high aspect ratios of elements, and very large radius-to-thickness ratios of shells. For verification of the proposed model, some benchmark laminated shell problems have been solved as compared to the numerical results obtained by the conventional h-convergent finite element method and other p-convergent analyses that used the Lagrange type polynomials as a shape function. Numerical results show that the proposed model is capable of prediction in-plane stresses around the crack tip as well as interlaminar stresses at the interface between shell layers.