A smoothed natural neighbour Galerkin method for flexoelectric solids

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-01 DOI:10.1615/intjmultcompeng.2024053300

Juanjuan Li, Shenjie Zhou

引用次数: 0

Abstract

In this paper, a smoothed natural neighbour Galerkin method is developed for modeling flexoelectricity in dielectric solids. The domain integrals in the weak form are implemented on the background Delaunay triangle meshes. Each Delaunay triangle is divided into four sub-domains. In each sub-domain, by introducing the gradient smoothing technique, the rotation gradients, and the electric field gradients can be represented as the first-order gradients of the displacement and the electric potential, respectively. Thus, the continuity requirement for the field variables is reduced from C1 to C0, and the integrals within the sub-domains are converted to the line integrals on the boundary. Then, the field variables are approximated via the non-Sibsonian partition of unity scheme, which enables the direct imposition of the essential boundary conditions. The proposed method is validated through examples with analytical solutions. Results show that the numerical solutions agree well with the analytical solutions.

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柔电固体的平滑自然邻域 Galerkin 方法

本文开发了一种平滑自然邻域 Galerkin 方法，用于电介质固体的挠电建模。弱形式的域积分是在背景 Delaunay 三角网格上实现的。每个 Delaunay 三角形划分为四个子域。在每个子域中，通过引入梯度平滑技术，旋转梯度和电场梯度可分别表示为位移和电动势的一阶梯度。因此，场变量的连续性要求从 C1 降为 C0，子域内的积分转换为边界上的线积分。然后，通过非西布森统一分割方案对场变量进行近似，这样就可以直接施加必要的边界条件。建议的方法通过实例与分析解进行了验证。结果表明，数值解与分析解十分吻合。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.