An efficient two-dimensional shear-lag model for the analysis of patched laminates

Fiber patch placement (FPP) is a manufacturing technique for variable stiffness composites. In the FPP approach, a structural component is assembled from a multitude of discrete fiber patches, thus allowing for an easy tailoring of the layup to the local load state. However, due to the discontinuous fibers at the patch edges, complex stress distributions occur in patched laminates. To date, an efficient method for the analysis of patched laminates on macro-scale does not exist. This article introduces a 2D planar shear-lag model (SLM) based on thin-plate mechanics and a simplified interlaminar shear stress formulation. It is shown how the governing partial differential equation system is assembled and how boundary conditions are set. The model is solved numerically using the Finite Element Method. For verification the 2D SLM is compared to a full 3D linear-elastic solution. It can be shown that the SLM allows for accurate prediction of stress fields disturbed by interrupted fibers with considerably improved numerical efficiency. An application example shows that the SLM resolves the effects of discontinuities significantly better than a state-of-the-art shell element modeling approach. As a consequence, a substantial progress in the design of patch laminated structures is achieved.