This study presents a multi-objective topology optimization method tailored to structures fabricated from functionally graded materials (FGMs), coated FGMs, and coated fiber-reinforced composite materials (FRCMs) with fixed fiber thickness. The design objective is the simultaneous minimization of elastic and thermal compliance. The material properties of these composite materials were derived to generate datasets using the representative volume element method under periodic boundary conditions. Subsequently, machine learning modules were developed based on the datasets to combine with the design process. The multi-objective optimization problem was addressed using the weighted sum method ensuring the generation of the Pareto front. The adaptive weighting strategy is employed to avoid biased results toward a single objective function. To define the coated boundaries within the design domain, image post-processing techniques such as convolution filters, interpolation schemes, and erosion methods were employed on the material layout information of the optimized FGM structures. Through numerical examples, optimized material layouts for coated assemblies incorporating FGMs and FRCMs are presented, with the performance verified through objective function values.

中文翻译：

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考虑功能梯度材料和涂层纤维增强的多目标拓扑设计


本研究提出了一种多目标拓扑优化方法，该方法适用于由功能梯度材料 （FGM）、涂层 FGM 和具有固定纤维厚度的涂层纤维增强复合材料 （FRCM） 制成的结构。设计目标是同时最小化弹性和热柔度。这些复合材料的材料属性被推导出来，以在周期性边界条件下使用代表性体积元法生成数据集。随后，基于数据集开发了机器学习模块，以与设计过程相结合。使用加权和方法解决了多目标优化问题，确保生成 Pareto 前沿。采用自适应加权策略来避免结果偏向单个目标函数。为了定义设计域内的涂层边界，对优化后的 FGM 结构的材料布局信息采用了图像后处理技术，例如卷积滤波器、插值方案和侵蚀方法。通过数值示例，提出了包含 FGM 和 FRCM 的涂层组件的优化材料布局，并通过目标函数值验证了性能。