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：丝束导向技术，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。因此，设计人员可以根据结构内的预期局部应力状态，局部调整丝束取向，从而（例如）优化丝束的强刚度方向以提供最大的力学效益。丝束路径优化可以成为自动化该设计过程的有效工具，但往往会产生可能难以制造的复杂设计。在丝束导向的背景下，这些复杂性可能表现为丝束起皱、间隙、重叠等缺陷。在本工作中，我们在丝束路径优化公式中引入制造约束，以限制最小丝束转弯半径以及丝束间间隙和重叠的最大密度。这是通过约束与丝束取向相关的矢量场的局部旋度和散度值来实现的。由此产生的局部约束通过增广拉格朗日法在优化框架中得到有效实施。该优化方法通过设计二维和三维结构得到验证，这些结构具有优化的丝束取向路径，在考虑不同级别制造限制的情况下最大化刚度（最小化柔度）。优化后的丝束路径显示出结构高效性并遵守了施加的制造约束。正如预期，原料丝束和铺放技术能够实现的几何复杂度越高，最终优化设计的刚度也越高。