Continuous fiber path optimization in additive manufacturing: A gradient-based B-spline finite element approach

Additive manufacturing of continuous fiber enables the control of local material distribution and mechanical characteristics. This localized control is realized through fiber path generation and optimization, which is one of the core problems in the additive manufacturing of continuous fiber. Current fiber path generation and optimization methods mostly try to infill topology-optimized parts or align the fiber with the maximum stress directions, which may lead to sub-optimality or time-consuming computations. This paper provides a different approach to optimize the fiber path directly by parameterizing it with B-splines and manipulating its control points. A finite element model with B-spline fiber parameterization is established, with an analytical fiber-in-element probability. This framework streamlines the computation of local and global stiffness and mass matrices, enabling effective and efficient prediction of loading responses, stiffness, and natural frequencies. The probability framework also allows efficient calculation of the gradients of the stiffness and mass matrices, leading to a gradient-based fiber path optimization. The effectiveness and accuracy of both the finite element and optimization methods are verified with simulation and experiment case studies. Results demonstrate enhancements in stiffness and strength with less fiber usage compared to a commonly adopted principal stress direction method. [Display omitted]