Concurrent level set topology and fiber orientation optimization of fiber-reinforced composite structures

By altering the structural shape and fiber orientation, this research aims to optimize the design of Fiber-Reinforced Composite (FRC) structures. The structural geometry is represented by a level set function approximated by quadratic B-spline functions. The fiber orientation field is parameterized with quadratic/cubic B-splines on hierarchically refined meshes. Different levels for B-spline mesh refinement for the level set and fiber orientation fields are studied to resolve geometric features and to obtain a smooth fiber layout. To facilitate FRC manufacturing, the parallel alignment and smoothness of fiber paths are enforced by introducing penalty terms referred to as "misalignment penalty" and "curvature penalty". A geometric interpretation of these penalties is provided. The material behavior of the FRCs is modeled by the Mori-Tanaka homogenization scheme and the macroscopic structure response is predicted by linear elasticity under static multiloading conditions. The governing equations are discretized by a Heaviside-enriched eXtended IsoGeometric Analysis (XIGA) to avoid the need to generate conformal meshes. Instabilities in XIGA are mitigated by the face-oriented ghost stabilization technique. This work considers mass and strain energy in the formulation of the optimization objective, along with misalignment and curvature penalties and additional regularization terms. Constraints are imposed on the volume of the structure. The resulting optimization problems are solved by a gradient-based algorithm. The design sensitivities are computed by the adjoint method. Numerical examples demonstrate with two-dimensional and three-dimensional configurations that the proposed method is efficient in simultaneously optimizing the macroscopic shape and the fiber layout while improving manufacturability by promoting parallel and smooth fiber paths.