Generation of Tow Paths on a Curved Shell in Three-Dimensional Space for Fiber Steering

A multimesh framework to optimize two-dimensional, flat-steered fiber laminates for a given loading condition is extended to include complex curved laminates in three-dimensional (3D) space. The optimal fiber angle distribution solution is used by a tow path planner to generate (steered) tow paths in curved laminates in 3D space. The framework utilizes two meshes in the optimization step: i) a coarse quadrilateral element-based manufacturing mesh (MM) used to discretize the fiber angle distributions with nodal values; and ii) a fine triangular element-based stress mesh used in the finite-element-based stress analysis to ensure a converged solution. Lagrangian interpolation functions are used to determine the fiber angles at the centroid of each finite element analysis (FEA) mesh element within a given MM. The number of design variables is minimized without jeopardizing the accuracy of the FEA solution. A third mesh, the tessellation mesh, is used to project the generated tow paths onto the curved laminates in 3D space accurately. This paper presents all the steps needed to go from optimized fiber angles to tow paths. In conclusion, a methodology is proposed and implemented to optimize variable-stiffness laminates on complex curved structures.