DGTO: Derivable geodesics-coupled topology optimization for multi-axis 3D printing of continuous fiber-reinforced spatial structures

Abstract

Continuous fiber reinforced composites (CFRCs) are composite materials with exceptional mechanical properties to enhance structural mechanical performance. In comparison with traditional three-axis 3D printing (also referred to as 2.5D printing), multi-axis 3D printing simultaneously moves the nozzle and rotates the build platform during the printing process, making it particularly suited for fabricating spatial structures made of CFRCs due to better alignment between the fiber depositions and principal stress directions. In this research, we propose a Derivable Geodesics-coupled Topology Optimization (DGTO) method for design of CFRCs given the manufacturing scheme of multi-axis 3D printing. A prominent feature of DGTO is the introduction of two geodesic fields to achieve curved layer generation and continuous fiber path planning. The heat diffusion equation and Poisson equation are solved to produce the geodesic fields, and hence, all objective functions and constraints related to the slices and paths are derivable, making them perfectly suitable to be integrated with topology optimization. Hence, the proposed method concurrently optimizes the density field and the auxiliary geodesic fields, simultaneously tuning the material distribution and spatial fiber distribution, thereby attaining optimal performance while fulfilling the manufacturing constraints of multi-axis printing, i.e., self-support of structure and overlap/gap-free of continuous fibers. Four numerical examples are presented to demonstrate the effectiveness of the algorithm, especially showing outstanding performances than designs for traditional three-axis 3D printing.