Structural lightweight is a core technical requirement for the structural design of aerospace and new energy power equipment structures. For multi-scale variable stiffness design optimization of discrete fiber-reinforced composite laminates, one of the challenges is how to avoid the explosion of design variable combinations caused by the increase in the number of candidate discrete fiber laying angles. The Normal Distribution Fiber Optimization (NDFO) interpolation scheme has the numerical advantage that the number of design variables does not increase with an increase in the number of candidate discrete fiber laying angles. However, the traditional NDFO interpolation scheme uses uniform penalty parameters across all elements, which means that normalizing the penalty parameters for all the elements ignores the convergence differences of discrete fiber laying angles in different elements within the macro-scale structure topology. This leads to time-consuming and unstable optimization iteration of the macro-scale structural topology and micro-scale discrete fiber laying angle selection. Especially, it easily causes the micro-scale discrete fiber laying angle selection to fall into the local optimum prematurely. Therefore, considering the difficulties and challenges of the traditional NDFO interpolation scheme in the multi-scale variable stiffness design optimization of fiber-reinforced composites. This paper proposes an Adaptive Normal Distribution Fiber Optimization (ANDFO) interpolation scheme, and the feedback mechanism of the convergence rate of the element design variable and the objective function is introduced to achieve the adaptive reduction of the penalty parameters. Based on the proposed ANDFO interpolation scheme, a multi-scale design optimization model of fiber-reinforced composite laminates is established, considering the macro-scale structure topology and micro-scale discrete fiber laying angel selection. The explicit sensitivity of the objective function of minimizing structural compliance to the macro-scale topological design variables and the micro-scale fiber laying angle design variables is derived. Considering the manufacturability of additive manufacturing based on the optimized design results, a multi-scale nonlinear continuous filtering strategy for discrete fiber laying angle is adopted to improve the continuity of the local fiber laying path. Numerical examples systematically present the coupling effects of macro-scale structural topology and micro-scale fiber laying path, multi-scale nonlinear discrete fiber continuous filtering laying path structure, and continuous fiber additive manufacturing multi-scale optimized structure. The proposed ANDFO scheme provides a new theoretical and methodological approach for the lightweight and integrated multi-scale design and manufacturing of fiber-reinforced composite laminates through additive manufacturing technology.

中文翻译：

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基于最小结构柔度和增材制造的自适应正态分布纤维优化方案的纤维增强复合材料并行多尺度设计优化


结构轻量化是航空航天与新能源动力装备结构设计的核心技术要求。对于离散纤维增强复合材料层合板的多尺度可变刚度设计优化，挑战之一是如何避免因候选离散纤维铺设角度数量增加而导致的设计变量组合爆炸。正态分布光纤优化 （NDFO） 插值方案具有数值优势，即设计变量的数量不会随着候选离散光纤铺设角度数量的增加而增加。然而，传统的 NDFO 插值方案在所有单元中使用统一的惩罚参数，这意味着归一化所有单元的惩罚参数会忽略宏观尺度结构拓扑中不同单元中离散光纤铺设角度的收敛差异。这导致了宏观结构拓扑和微观离散光纤铺设角度选择的耗时且不稳定的优化迭代。特别是，它容易导致微尺度离散光纤铺设角度选择过早地陷入局部最优。因此，考虑到传统NDFO插值方案在纤维增强复合材料多尺度变刚度设计优化中的困难和挑战。该文提出了一种自适应正态分布纤维优化 （ANDFO） 插值方案，并引入单元设计变量和目标函数收敛速率的反馈机制，以实现惩罚参数的自适应折减。 基于所提出的 ANDFO 插值方案，考虑了宏观结构拓扑和微观离散纤维铺设角度选择，建立了纤维增强复合材料层合板的多尺度设计优化模型。推导了最小化结构柔度的目标函数对宏观尺度拓扑设计变量和微观纤维铺设角设计变量的显式敏感性。在优化设计结果的基础上考虑增材制造的可制造性，采用离散光纤铺设角度的多尺度非线性连续滤波策略，以提高局部光纤铺设路径的连续性。数值算例系统地阐述了宏观结构拓扑与微观纤维铺设路径、多尺度非线性离散纤维连续滤波铺设路径结构、连续纤维增材制造多尺度优化结构的耦合效应。所提出的 ANDFO 方案为通过增材制造技术实现纤维增强复合材料层合板的轻量化和集成多尺度设计和制造提供了一种新的理论和方法论方法。