{"title":"Meshless Non-Parametric Shape Design of Piecewise Approximately Developable Surfaces Using Discretized Local Gauss Map","authors":"K. Hayakawa, M. Ohsaki, Jingyao Zhang","doi":"10.20898/j.iass.2022.023","DOIUrl":null,"url":null,"abstract":"A meshless and non-parametric approach is proposed for shape design of curved surfaces consisting of approximately developable surface patches. A local Gauss map is defined at the grid point of a surface, and its developability is evaluated based on the area of the local Gauss map. An optimization problem is formulated for minimizing the sum of square areas of the local Gauss map at the grid points of the surface with specified boundary shape. Internal boundaries between the approximately developable surface patches are generated by relaxing the developability at the selected grid points. The effectiveness of the proposed method for generating various shapes of piecewise approximately developable surface is demonstrated in the numerical examples.","PeriodicalId":42855,"journal":{"name":"Journal of the International Association for Shell and Spatial Structures","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the International Association for Shell and Spatial Structures","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.20898/j.iass.2022.023","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, CIVIL","Score":null,"Total":0}
引用次数: 0
Abstract
A meshless and non-parametric approach is proposed for shape design of curved surfaces consisting of approximately developable surface patches. A local Gauss map is defined at the grid point of a surface, and its developability is evaluated based on the area of the local Gauss map. An optimization problem is formulated for minimizing the sum of square areas of the local Gauss map at the grid points of the surface with specified boundary shape. Internal boundaries between the approximately developable surface patches are generated by relaxing the developability at the selected grid points. The effectiveness of the proposed method for generating various shapes of piecewise approximately developable surface is demonstrated in the numerical examples.
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The Association publishes an international journal, the Journal of the IASS, four times yearly, in print (ISSN 1028-365X) and on-line (ISSN 1996-9015). The months of publication are March, June, September and December. Occasional extra electronic-only issues are included in the on-line version. From this page you can access one or more issues -- a sample issue if you are not logged into the members-only portion of the site, or the current issue and several back issues if you are logged in as a member. For any issue that you can view, you can download articles as .pdf files.
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