Design support of a developable surface considering its bending energy
A method to design a developable surface and its developed shape is proposed. A developable surface, which is generated by sweeping a straight line along a three-dimensional curve, can be seen many products such as ships, buildings, clothes, and so on. Although it is important to design the surface...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | Japanese |
| Published: |
The Japan Society of Mechanical Engineers
2020-09-01
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| Series: | Nihon Kikai Gakkai ronbunshu |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/transjsme/86/891/86_20-00169/_pdf/-char/en |
| _version_ | 1828193536845021184 |
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| author | Kotaro YOSHIDA Hidefumi WAKAMATSU Eiji MORINAGA Takahiro KUBO |
| author_facet | Kotaro YOSHIDA Hidefumi WAKAMATSU Eiji MORINAGA Takahiro KUBO |
| author_sort | Kotaro YOSHIDA |
| collection | DOAJ |
| description | A method to design a developable surface and its developed shape is proposed. A developable surface, which is generated by sweeping a straight line along a three-dimensional curve, can be seen many products such as ships, buildings, clothes, and so on. Although it is important to design the surface in case that designers give some constraints, its design process is not automated because of the difficulty of its modeling. Especially, cloth products are required to design not only their three-dimensional shapes but also their developed shapes. Therefore, we aim to propose a method to design the surface satisfying some constraints and its developed shape. As an example, we assume that some constraints are related to the control points of a curve in a developable surface. In this paper, it is revealed that the direction of a generatrix can be determined geometrically when a pair of three-dimensional curves are given. Moreover, in order to obtain a steadier shape, not only this condition but also the potential energy of the surface should be considered. From the above, we formulate optimization problems, upon this design process, which have different objective functions: one is the condition of a developable surface and the other is its bending energy. We compared and examined bending energies and maximum principal curvatures obtained by two different optimization problems. In order to verify our proposed method, we performed an experiment and confirmed its validity. |
| first_indexed | 2024-04-12T09:10:12Z |
| format | Article |
| id | doaj.art-2b25003f76a846979f25a9240b1fb0c6 |
| institution | Directory Open Access Journal |
| issn | 2187-9761 |
| language | Japanese |
| last_indexed | 2024-04-12T09:10:12Z |
| publishDate | 2020-09-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Nihon Kikai Gakkai ronbunshu |
| spelling | doaj.art-2b25003f76a846979f25a9240b1fb0c62022-12-22T03:39:00ZjpnThe Japan Society of Mechanical EngineersNihon Kikai Gakkai ronbunshu2187-97612020-09-018689120-0016920-0016910.1299/transjsme.20-00169transjsmeDesign support of a developable surface considering its bending energyKotaro YOSHIDA0Hidefumi WAKAMATSU1Eiji MORINAGA2Takahiro KUBO3Dept. of Materials and Manufacturing Science, Graduate School of Eng., Osaka UniversityDept. of Materials and Manufacturing Science, Graduate School of Eng., Osaka UniversityGraduate School of Humanities and Sustainable System Sciences, Osaka Prefecture UniversityWacoal Holdings Corp.A method to design a developable surface and its developed shape is proposed. A developable surface, which is generated by sweeping a straight line along a three-dimensional curve, can be seen many products such as ships, buildings, clothes, and so on. Although it is important to design the surface in case that designers give some constraints, its design process is not automated because of the difficulty of its modeling. Especially, cloth products are required to design not only their three-dimensional shapes but also their developed shapes. Therefore, we aim to propose a method to design the surface satisfying some constraints and its developed shape. As an example, we assume that some constraints are related to the control points of a curve in a developable surface. In this paper, it is revealed that the direction of a generatrix can be determined geometrically when a pair of three-dimensional curves are given. Moreover, in order to obtain a steadier shape, not only this condition but also the potential energy of the surface should be considered. From the above, we formulate optimization problems, upon this design process, which have different objective functions: one is the condition of a developable surface and the other is its bending energy. We compared and examined bending energies and maximum principal curvatures obtained by two different optimization problems. In order to verify our proposed method, we performed an experiment and confirmed its validity.https://www.jstage.jst.go.jp/article/transjsme/86/891/86_20-00169/_pdf/-char/endesignmodelingdevelopable surfaceoptimizationautomation |
| spellingShingle | Kotaro YOSHIDA Hidefumi WAKAMATSU Eiji MORINAGA Takahiro KUBO Design support of a developable surface considering its bending energy Nihon Kikai Gakkai ronbunshu design modeling developable surface optimization automation |
| title | Design support of a developable surface considering its bending energy |
| title_full | Design support of a developable surface considering its bending energy |
| title_fullStr | Design support of a developable surface considering its bending energy |
| title_full_unstemmed | Design support of a developable surface considering its bending energy |
| title_short | Design support of a developable surface considering its bending energy |
| title_sort | design support of a developable surface considering its bending energy |
| topic | design modeling developable surface optimization automation |
| url | https://www.jstage.jst.go.jp/article/transjsme/86/891/86_20-00169/_pdf/-char/en |
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