Geometrically nonlinear topology optimization of porous structures

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Engineering Analysis with Boundary Elements Pub Date : 2024-11-06 DOI:10.1016/j.enganabound.2024.106014

Yongfeng Zheng, Rongna Cai, Jiawei He, Zihao Chen

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Abstract

Porous structures are extensively used in engineering, and current designs of porous structures are constructed based on linear assumptions. In engineering, deformation cannot be ignored, so it is necessary to consider the effect of geometric nonlinearity in structural design. For the first time, this paper performs the geometrically nonlinear topology optimization of porous structures. This paper presents the theory of geometric nonlinear analysis, the bi-directional evolutionary method is used to search for the topological configurations of porous structures, the number of structural holes is determined by the number of periodicities. Furthermore, the optimization equation, sensitivity analysis, and optimization process are provided in detail. Lastly, four numerical examples are investigated to discuss the influence of geometric nonlinearity on the design of porous structures, such as comparisons between geometric nonlinear and linear design, the ability of geometric nonlinear design to resist cracks, changes in load amplitude and position and 3D porous designs. The conclusions drawn can provide strong reference for the design of high-performance porous structures.

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多孔结构的几何非线性拓扑优化

多孔结构在工程中应用广泛，而目前的多孔结构设计都是基于线性假设。在工程中，变形是不容忽视的，因此有必要在结构设计中考虑几何非线性的影响。本文首次对多孔结构进行了几何非线性拓扑优化。本文提出了几何非线性分析理论，采用双向进化法寻找多孔结构的拓扑构型，结构孔数由周期数决定。此外，还详细介绍了优化方程、灵敏度分析和优化过程。最后，通过四个数值实例探讨了几何非线性对多孔结构设计的影响，如几何非线性设计与线性设计的比较、几何非线性设计的抗裂能力、载荷振幅和位置的变化以及三维多孔结构设计。所得出的结论可为高性能多孔结构的设计提供有力的参考。

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

Engineering Analysis with Boundary Elements 工程技术-工程：综合

CiteScore

5.50

自引率

18.20%

发文量

368

审稿时长

56 days

期刊介绍： This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.