Tow steering technologies, such as Automated fiber placement, enable the fabrication of composite laminates with curvilinear fiber, tow, or tape paths. Designers may therefore tailor tow orientations locally according to the expected local stress state within a structure, such that strong and stiff orientations of the tow are (for example) optimized to provide maximal mechanical benefit. Tow path optimization can be an effective tool in automating this design process, yet has a tendency to create complex designs that may be challenging to manufacture. In the context of tow steering, these complexities can manifest in defects such as tow wrinkling, gaps, overlaps. In this work, we implement manufacturing constraints within the tow path optimization formulation to restrict the minimum tow turning radius and the maximum density of gaps between and overlaps of tows. This is achieved by bounding the local value of the curl and divergence of the vector field associated with the tow orientations. The resulting local constraints are effectively enforced in the optimization framework through the Augmented Lagrangian method. The resulting optimization methodology is demonstrated by designing 2D and 3D structures with optimized tow orientation paths that maximize stiffness (minimize compliance) considering various levels of manufacturing restrictions. The optimized tow paths are shown to be structurally efficient and to respect imposed manufacturing constraints. As expected, the more geometrical complexity that can be achieved by the feedstock tow and placement technology, the higher the stiffness of the resulting optimized design.

翻译：自动铺丝技术（如自动纤维铺放）能够制造具有曲线纤维、丝束或带材路径的复合材料层合板。设计者可根据结构内部预期局部应力状态，定制纤维丝束的局部方向，从而优化纤维取向（例如）以实现最大力学效益。丝束路径优化可作为自动化设计流程的有效工具，但易产生难以制造的复杂设计。在自动铺丝背景下，此类复杂性可能表现为纤维褶皱、间隙、重叠等缺陷。本研究在丝束路径优化框架中引入制造约束，限制最小丝束转弯半径及丝束间间隙与重叠的最大密度。通过约束与丝束取向相关向量场的局部旋度和散度值实现上述限制，并采用增广拉格朗日法在优化框架中有效施加这些局部约束。通过设计考虑不同制造限制的二维及三维结构（以丝束优化取向路径最大化刚度即最小化柔度），验证所提优化方法。结果表明，优化后的丝束路径兼具结构效率且满足预设制造约束。正如预期，原料丝束与铺放技术可实现的几何复杂度越高，最终优化设计的刚度越大。