Isogeometric topology optimization for maximizing band gap of two-dimensional phononic crystal structures

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling Pub Date : 2024-09-11 DOI:10.1016/j.apm.2024.115702

Shuohui Yin , Jiahui Huang , Sisi Liu , Shuitao Gu , Tinh Quoc Bui , Ziheng Zhao

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Abstract

A smooth and efficient isogeometric topology optimization (ITO) method for maximizing band gaps in two-dimensional phononic crystals is developed in the paper. The band gaps of phononic crystals are computed by the NURBS-based isogeometric analysis, and the material distributions of two-dimensional phononic crystals are represented by the smooth, high-order continuity of the NURBS surface. The densities defined at each control point of the NURBS surface are employed as optimized design variables. The isogeometric analysis optimization using the same spline technique for both geometry and numerical analysis can benefit the optimization procedure and obtain smooth optimized structures, which can be easily used in 3D printing. The maximizing band gaps of phononic crystals for both out-of-plane and in-plane wave modes are obtained here using the present ITO approach. Numerical examples validated the effectiveness and reliability of the ITO method in broadening the band gaps and finding the optimal phononic crystals. And the numerical results show that the smooth optimized structures are obtained with fewer iterations.

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等几何拓扑优化，实现二维声子晶体结构带隙最大化

本文提出了一种平滑高效的等几何拓扑优化（ITO）方法，用于最大化二维声子晶体的带隙。声子晶体的带隙由基于 NURBS 的等几何分析计算得出，二维声子晶体的材料分布由 NURBS 表面的平滑高阶连续性表示。在 NURBS 曲面的每个控制点上定义的密度被用作优化设计变量。在几何和数值分析中使用相同的样条线技术进行等几何分析优化，有利于优化过程，并能获得平滑的优化结构，便于在三维打印中使用。在这里，利用现有的 ITO 方法获得了声子晶体平面外和平面内波模式的最大带隙。数值实例验证了 ITO 方法在拓宽带隙和寻找最佳声波晶体方面的有效性和可靠性。数值结果表明，以较少的迭代次数就能获得平滑的优化结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematical Modelling 数学-工程：综合

CiteScore

9.80

自引率

8.00%

发文量

508

审稿时长

43 days

期刊介绍： Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged. This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering. Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.