An isogeometric framework for the modeling of curvilinear anisotropic media

Abstract

The advent of multi-material additive manufacturing and automated composite manufacturing has enabled the design of structures featuring complex curvilinear anisotropy. To take advantage of the new design space, efficient computational approaches are quintessential. In this study, we explored a new NURBS-based Isogeometric Analysis (IGA) framework for the simulation of curvilinear fiber composites and we compared it to standard Finite Element Analysis (FEA).We showed that, thanks to the exact geometric representation and the enriched continuity between elements, NURBS-based IGA outperforms classical FEA in terms of computational efficiency, run-time, and estimation quality of field variables for the same number of degrees-of-freedom. To further demonstrate the use of the IGA framework, we performed optimization studies aimed at identifying the fiber paths minimizing stress concentration and Tsai-Wu failure index. The model showed that curvilinear anisotropy can be effectively harnessed to reduce the stress concentration of up to 82% compared to unidirectional composites without affecting the overall plate stiffness significantly.