Full sensitivity-driven gap/overlap free design of carbon fiber-reinforced composites for 3D printing

Abstract This paper presents a mathematically stringent method for gap/overlap free design of carbon fiber-reinforced composites for 3D printing. The proposed method employs signed distance level set function to represent the fiber paths by extracting the equidistant iso-level set profiles, through which neighbouring fiber paths keep a constant distance, eliminating the gap and overlap defects of existing methods that generate fiber paths from discretely defined fiber angle variables. Then, a compliance minimization fiber path optimization problem is formulated under the level set framework for optimal fiber-reinforcement design. A major contribution lies in the solution of the optimization problem. The adjoint sensitivity analysis is performed to derive the gradient information for fiber path design update. More importantly, the domain integral term inside the sensitivity result is transformed into a boundary integral expression facilitated by extraction of the structural skeletons and rays. Hence, the full sensitivity result is derived instead of eliminating the non-executable domain integral terms in existing studies, which results in even faster and more stable convergence. A few numerical examples are studied to demonstrate the effectiveness of the proposed fiber path optimization method. 3D printing and mechanical testing results validate the optimized fiber-reinforcement effect, as well as the manufacturability improvement by avoiding gap and overlap defects.