A non-uniform rational B-splines (NURBS) based optimization method for fiber path design

Abstract

This work presents a systematic optimization method utilizing non-uniform rational B-splines (NURBS) to represent fibers in composites and design their paths. Beyond mean compliance, the objective function incorporates repulsive energy to prevent fiber knots and intersections. Utilizing NURBS control points as design variables reduces the number of design variables and expands the solution space, as they can reach any point within the design domain under the guidance of the sensitivity of the objective function in the method of moving asymptotes. Additionally, the p-norm technique for curvature constraints represents an innovative adaptation to avoid sharp turns in fibers. The work can also add fibers during optimization and enable the design of multi-layer fiber-enhanced composite structure to address various design challenges associated with optimizing fiber paths. Numerical examples show that the mean compliance decreases by 60∼70 % compared to initial configurations, and the computation time is reduced by 80 % compared to similar cases in prior work.