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This paper presents an effective fiber angle optimization method for two and multi-layered variable stiffness composites. A gradient-based fiber angle optimization method is developed based on isogeometric analysis (IGA). Firstly, the element densities and fiber angles for two and multi-layered composites are synchronously optimized using an extended Bi-layered continuous fiber angle optimization method (XBi-CFAO). The densities and fiber angles in the base layer are attached to the control points. The structure response and sensitivity analysis are accomplished using the non-uniform rational B-spline (NURBS) based IGA. By the benefit of the B-spline space, this method is free from checkerboards, and no additional filtering is needed to smooth the sensitivity numbers. Then the curved fiber paths are generated using the streamline method and the discontinuous fiber paths are smoothed using a partitioned selection process. The proposed method in the paper can alleviate the phenomenon of fiber discontinuity, enhance information retention for the optimized fiber angles of the singular points and save calculating resources effectively.

An XBi-CFAO Method for the Optimization of Multi-Layered Variable Stiffness Composites Using Isogeometric Analysis