Continuous fiber fused filament fabrication (CF4) is a layer-by-layer additive manufacturing technique that deposits continuous fiber fused filaments (CFFFs) with a significant in-plane variation of the fiber trajectory, thereby offering great flexibility in fabricating variable-stiffness composite laminates (VSCLs). We introduce a topology optimization method for the design of additively manufactured VSCLs made of overlapping, fiber-reinforced bars. The proposed method is based on geometry projection (GP) techniques, whereby the bars are represented by high-level geometric primitives. As in other GP techniques, this high-level parameterization is mapped onto a fixed structured finite element mesh for conducting analysis, as in density-based topology optimization techniques. However, unlike previous GP techniques that have demonstrated their applicability in designing structures as assemblies of individual fiber-reinforced components, this work focuses on the design of composite structures that adhere to CF4 manufacturing processes. Therefore, we first formulate a material interpolation scheme that better captures the stiffness at the composite’s joints obtained from bar overlaps as a stack. Second, the proposed material interpolation employs composite laminate theory to capture the in-plane and out-of-plane behavior of the structure. Third, to produce designs that conform to the CF4 process, we also proposed a novel length constraint formulation in the form of penalization on the projection scheme, which ensures a minimum length for all the bars. This minimum length limit does not require adding a constraint to the optimization problem. The efficacy and efficiency of the proposed method are demonstrated by a series of compliance minimization problems with in-plane and/or out-of-plane loading. The methodology is also applied to the design of a displacement inverter compliant mechanism.

中文翻译：

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一种用于增材制造可变刚度复合材料层合板拓扑优化的几何投影方法


连续纤维熔丝制造 （CF4） 是一种逐层增材制造技术，可沉积具有显着纤维轨迹面内变化的连续纤维熔丝 （CFFF），从而为制造可变刚度复合材料层压板 （VSCL） 提供极大的灵活性。我们介绍了一种拓扑优化方法，用于设计由重叠的纤维增强棒制成的增材制造 VSCL。所提出的方法基于几何投影 （GP） 技术，其中条形由高级几何基元表示。与其他 GP 技术一样，这种高级参数化被映射到固定结构的有限元网格上以进行分析，就像基于密度的拓扑优化技术一样。然而，与以前的 GP 技术不同，这些技术已经证明其在将结构设计为单个纤维增强组件的组件方面的适用性，这项工作的重点是设计符合 CF4 制造工艺的复合结构。因此，我们首先制定一个材料插值方案，以更好地捕获从杆重叠（堆栈）中获得的复合材料接头处的刚度。其次，所提出的材料插值采用复合材料层压板理论来捕获结构的面内和面外行为。第三，为了生成符合 CF4 流程的设计，我们还提出了一种新的长度约束公式，其形式是对投影方案进行惩罚，从而确保所有杆材的最小长度。此最小长度限制不需要向优化问题添加约束。 所提出的方法的有效性和效率通过面内和/或面外载荷的一系列柔度最小化问题来证明。该方法也适用于位移逆变器兼容机构的设计。