3D auxetic linkage based on Kirigami

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design Pub Date : 2024-04-23 DOI:10.1016/j.cagd.2024.102296

Xiaopeng Sun , Shihan Liu , Zhiqiang Luo , Zhongtai Yang

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引用次数: 0

Abstract

The structural design of 3D auxetic linkages is a burgeoning field in digital manufacturing. This article presents a novel algorithm for designing 3D auxetic linkage structures based on Kirigami principles to address existing limitations. The 3D input model is initially mapped to a 2D space using conformal mapping based on the BFF method. This is followed by 2D re-meshing using an equilateral triangle mesh. Subsequently, a 3D topological mesh of the auxetic linkage is calculated through inverse mapping based on directed area. We then introduce new basic rotating and non-rotating units, employing them as the initial structure of the 3D auxetic linkage in accordance with Kirigami techniques. Lastly, a deformation energy function is defined to optimize the shape of the rotating units. The vertex coordinates of the non-rotating units are updated according to the optimized positions of the rotating units, thereby generating an optimal 3D auxetic linkage structure. Experimental results validate the effectiveness and accuracy of our algorithm. Quantitative analyses of structural porosity and optimization accuracy, as well as comparisons with related works, indicate that our algorithm yields structures with smaller shape errors.

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基于桐纸的 3D 辅助连接装置

三维辅助连杆结构设计是数字制造领域的一个新兴领域。本文介绍了一种基于桐神原理的三维辅助连杆结构设计新算法，以解决现有的局限性。三维输入模型首先通过基于 BFF 方法的保角映射被映射到二维空间。然后使用等边三角形网格进行二维再映射。随后，通过基于有向面积的反映射，计算出辅助连接的三维拓扑网格。然后，我们引入了新的基本旋转和非旋转单元，并根据桐神技术将其用作三维辅助连杆的初始结构。最后，我们定义了变形能量函数，以优化旋转单元的形状。根据旋转单元的优化位置更新非旋转单元的顶点坐标，从而生成最佳的三维辅助连杆结构。实验结果验证了我们算法的有效性和准确性。对结构孔隙率和优化精度的定量分析，以及与相关工作的比较表明，我们的算法产生的结构形状误差较小。

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

Computer Aided Geometric Design 工程技术-计算机：软件工程

CiteScore

3.50

自引率

13.30%

发文量

审稿时长

60 days

期刊介绍： The journal Computer Aided Geometric Design is for researchers, scholars, and software developers dealing with mathematical and computational methods for the description of geometric objects as they arise in areas ranging from CAD/CAM to robotics and scientific visualization. The journal publishes original research papers, survey papers and with quick editorial decisions short communications of at most 3 pages. The primary objects of interest are curves, surfaces, and volumes such as splines (NURBS), meshes, subdivision surfaces as well as algorithms to generate, analyze, and manipulate them. This journal will report on new developments in CAGD and its applications, including but not restricted to the following: -Mathematical and Geometric Foundations- Curve, Surface, and Volume generation- CAGD applications in Numerical Analysis, Computational Geometry, Computer Graphics, or Computer Vision- Industrial, medical, and scientific applications. The aim is to collect and disseminate information on computer aided design in one journal. To provide the user community with methods and algorithms for representing curves and surfaces. To illustrate computer aided geometric design by means of interesting applications. To combine curve and surface methods with computer graphics. To explain scientific phenomena by means of computer graphics. To concentrate on the interaction between theory and application. To expose unsolved problems of the practice. To develop new methods in computer aided geometry.