Full-scale isogeometric topology optimization of freeform fiber-reinforced composite shells

Abstract

This paper proposes a full-scale isogeometric topology optimization (ITO) method based on Bézier extraction for design of freeform fiber-reinforced composite (FRC) shells. In this method, freeform shells are modeling by multiple NURBS patches, where a penalty method is introduced to enhance displacement and rotation continuity at the coupling interfaces between multiple NURBS patches. A multi-patch isogeometric Kirchhoff–Love shell model based on Bézier extraction is established for modeling and analysis of freeform FRC shell structures with high efficiency and precision. A multi-material topology optimization framework is adopted to simultaneously optimize the topology of the matrix material, the morphology and path of the fiber, where two sets of design variables are set at control points to describe the topology of composite and fiber materials, respectively. In full-scale ITO, a multi-material constraint strategy with a global volume constraint of the composite material and a local volume constraint of the fiber material is developed to promote the generation of slender, continuous and uniformly distributed fiber structure in the matrix material. Several numerical examples of compliance minimization are provided to validate the effectiveness of the proposed method. The optimized results indicate that the proposed method has a great design freedom and can obtain FRC shells with continuous fiber path on freeform surfaces.