Continuous Fiber Path Optimization in Composite Additive Manufacturing via a Finite Element Model With B-Spline Fiber Parameterization

Abstract This paper presents a finite element model of the additive manufactured part with continuous fiber reinforcement. The proposed model exploits the B-spline parameterization of the fiber path while approximating the fiber path within a triangular element to be a straight line. This simplification enables the analytical and computational-efficient calculation of the mechanical properties of the printed parts. The elements in the model are differentiated into three categories to account for the location of fiber: matrix elements, main fiber-reinforced elements, and secondary fiber-reinforced elements. Analytical formulas to calculate the geometry-dependent stiffness matrix are established. With the established finite element model with B-spline fiber parameterization, the continuous fiber path is optimized by manipulating the control points of the B-spline to reduce fiber usage while increasing the stiffness of the part. The parts with the reference and optimized carbon fiber paths are 3D printed with a continuous-fiber fused deposition method printer, with polylactic acid as the matrix material. The estimated mechanical properties of the printed parts have been verified via experimental tensile tests.