Concurrent level set and fiber orientation optimization of composite structures

Abstract

By adjusting both the structural shape and fiber orientation, this research aims to optimize the design of Fiber Reinforced Composite structures. The structural geometry is represented by a level set function, which is 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 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", which are incorporated into the optimization process. A geometric interpretation of the penalties is provided. The material behavior of the FRCs is modeled by the Mori-Tanaka homogenization scheme and the macroscopic structure response is modeled by linear elasticity under static mutiloading conditions. The Governing equations are discretized by a Heaviside-enriched eXtended IsoGeometric Analysis to avoid the need to generate conformal meshes. Instabilities in XIGA are mitigated by the facet-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.

Figures (27)

• Figure 1: Geometric description of solid ($\Omega_1$)/void ($\Omega_2$) design domain using the LSF.
• Figure 2: Fiber angle definitions in 3D ($\theta_{xy}$,$\theta_z$).
• Figure 3: Illustration of level set function for a truss structure (top left), the B-spline surface parameterizing the fiber orientation(top right), and the resulting fiber orientation and geometry (bottom).
• Figure 4: Enrichment strategy in XIGA.
• Figure 5: Matrix fiber layout for MT.