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| 基于降阶模型的二维声子晶体多目标拓扑优化 |
| Multi-objective Topology Optimization of Two-dimensional Phononic Crystals based on Reduced Model |
| 投稿时间：2025-09-28 修订日期：2025-12-03 |
| DOI： |
| 中文关键词: 声子晶体 等几何分析 降阶模型 非支配排序遗传算法 多目标拓扑优化 |
| 英文关键词:Phononic crystals Isogeometric analysis method Reduced model Non-dominated sorting genetic algorithm Multi-objective topology optimization |
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| 中文摘要: |
| 利用拓扑优化技术可设计出具有期望带隙特性且具备一定承载能力的声子晶体结构, 在振动、噪音控制等领域展现出极大的应用潜力。快速非支配排序遗传算法（NSGA-Ⅱ）作为一种全局优化方法已广泛应用于声子晶体拓扑优化，但其评估函数计算量大，严重制约整体计算效率。为改善该问题，提出了一种基于等几何分析方法和降阶模型的二维声子晶体多目标拓扑优化方法。以特定阶相对带隙宽度最大和结构柔度最小为优化目标，通过连通性分析引入限制孤立单元约束，利用非支配排序遗传算法对二维固体声子晶体进行了优化设计。通过数值算例验证了本文模型及方法的有效性和效率。结果表明在二维声子晶体中，问题的维度减少了91.4%，CPU时间减少了44.5%。优化结果在满足期望带隙的同时也兼顾到限制孤立单元要求和承载性要求。与常规有限元方法相比，实现了更低的计算维度和时间。 |
| 英文摘要: |
| Topology optimization enables the design of phononic crystal structures with desired band gap characteristics and adequate load-bearing capacity, showing great potential in applications such as vibration and noise control. The Non-dominated Sorting Genetic Algorithm II (NSGA-II), as a global optimization method, has been widely used in phononic crystal topology optimization. However, the high computational cost of evaluating objective functions significantly limits overall efficiency.To improve this problem, a multi-objective topology optimization approach for two-dimensional phononic crystals based on isogeometric analysis method and reduced model is proposed. The optimization objective is to maximize the relative bandgap width of a specific order and minimize the structural flexibility.A connectivity constraint is introduced based on topological analysis to suppress isolated material units. Numerical results validate the effectiveness and efficiency of the proposed method, demonstrating a 91.4% reduction in model dimensionality and a 44.5% decrease in CPU time. The optimized structures not only achieve the targeted band gap performance but also meet structural connectivity and load-bearing requirements. Compared to conventional finite element methods, the proposed approach offers significantly improved computational efficiency. |
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