Optimizing Fiber Orientation and Structural Shape of Composite Structures for Enhanced Performance

This research aims to optimize the design of Fiber Reinforced Composite (FRC) structures by simultaneously adjusting both the structural shape and fiber orientation. The structural geometry is represented using a level set function, while the fiber orientation field is parameterized with quadratic/cubic B-splines. Penalties for fiber misalignment and curvature are introduced to promote parallel and smooth fiber paths, facilitating manufacturing. The material behavior of the FRCs is modeled using the Mori-Tanaka homogenization scheme, and the macroscopic structure response is modeled by linear elasticity under static multiloading conditions. The governing equations are discretized using eXtended IsoGeometric Analysis (XIGA) to avoid the need for conformal meshes. The resulting optimization problems are solved using a gradient-based algorithm.