有限变形下挠性电的C0内罚有限元法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-06-25 DOI:10.1016/j.cma.2025.118133

Sergi Pérez-Escudero, Sonia Fernández-Méndez

{"title":"有限变形下挠性电的C0内罚有限元法","authors":"Sergi Pérez-Escudero, Sonia Fernández-Méndez","doi":"10.1016/j.cma.2025.118133","DOIUrl":null,"url":null,"abstract":"<div><div>The 4th-order partial differential equations modeling the flexoelectric effect at finite deformations are considered, accounting for direct and converse effects. Its numerical solution, using standard <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> Finite Elements, is carried out through the development of a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> Interior Penalty method (<span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span>-IPM) with a Newton–Raphson nonlinear solver. The simulation of metamaterials by means of generalized periodicity conditions is also addressed within the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span>-IPM framework. The order of convergence of the method is assessed in a synthetic test, studying the effect of the penalty parameters in the accuracy of the scheme. The method is also applied to the solution of a cantilever beam problem, and to the simulation of metamaterials at large deformations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118133"},"PeriodicalIF":7.3000,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A C0 Interior Penalty Finite Element method for flexoelectricity at finite deformations\",\"authors\":\"Sergi Pérez-Escudero, Sonia Fernández-Méndez\",\"doi\":\"10.1016/j.cma.2025.118133\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The 4th-order partial differential equations modeling the flexoelectric effect at finite deformations are considered, accounting for direct and converse effects. Its numerical solution, using standard <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> Finite Elements, is carried out through the development of a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> Interior Penalty method (<span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span>-IPM) with a Newton–Raphson nonlinear solver. The simulation of metamaterials by means of generalized periodicity conditions is also addressed within the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span>-IPM framework. The order of convergence of the method is assessed in a synthetic test, studying the effect of the penalty parameters in the accuracy of the scheme. The method is also applied to the solution of a cantilever beam problem, and to the simulation of metamaterials at large deformations.</div></div>\",\"PeriodicalId\":55222,\"journal\":{\"name\":\"Computer Methods in Applied Mechanics and Engineering\",\"volume\":\"444 \",\"pages\":\"Article 118133\"},\"PeriodicalIF\":7.3000,\"publicationDate\":\"2025-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Methods in Applied Mechanics and Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0045782525004050\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Methods in Applied Mechanics and Engineering","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0045782525004050","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

考虑了有限变形下挠曲电效应的四阶偏微分方程，考虑了正效应和逆效应。它的数值解，使用标准的C0有限元，通过发展C0内罚法（C0- ipm）与牛顿-拉夫森非线性求解器进行。在C0-IPM框架下，利用广义周期性条件对超材料进行了模拟。在综合测试中评估了该方法的收敛阶，研究了惩罚参数对方案精度的影响。该方法也适用于悬臂梁问题的求解和超材料大变形的模拟。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A C0 Interior Penalty Finite Element method for flexoelectricity at finite deformations

The 4th-order partial differential equations modeling the flexoelectric effect at finite deformations are considered, accounting for direct and converse effects. Its numerical solution, using standard

C^{0}

Finite Elements, is carried out through the development of a

C^{0}

Interior Penalty method (

C^{0}

-IPM) with a Newton–Raphson nonlinear solver. The simulation of metamaterials by means of generalized periodicity conditions is also addressed within the

C^{0}

-IPM framework. The order of convergence of the method is assessed in a synthetic test, studying the effect of the penalty parameters in the accuracy of the scheme. The method is also applied to the solution of a cantilever beam problem, and to the simulation of metamaterials at large deformations.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Computer Methods in Applied Mechanics and Engineering 工程技术-工程：综合

CiteScore

12.70

自引率

15.30%

发文量

719

审稿时长

44 days

期刊介绍： Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.