{"title":"A triangular fractal plate bending element","authors":"Marcelo Epstein, Philip Vernon","doi":"10.1007/s00033-024-02300-0","DOIUrl":null,"url":null,"abstract":"<p>The stiffness matrix of a structural Sierpiński triangle under conditions of transversal bending is presented. The derivation is based exclusively on considerations of symmetry, equilibrium, and self-similarity. As a result, the stiffness matrix is shown to depend on a single material parameter. An illustrative numerical example is presented on the basis of an ad hoc computer code for the assembled stiffness of an overall structure consisting of a grid of fractal elements.\n</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift für angewandte Mathematik und Physik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00033-024-02300-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The stiffness matrix of a structural Sierpiński triangle under conditions of transversal bending is presented. The derivation is based exclusively on considerations of symmetry, equilibrium, and self-similarity. As a result, the stiffness matrix is shown to depend on a single material parameter. An illustrative numerical example is presented on the basis of an ad hoc computer code for the assembled stiffness of an overall structure consisting of a grid of fractal elements.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
