The Isotropic Material Design of In-Plane Loaded Elasto-Plastic Plates
This paper puts forward a new version of the Isotropic Material Design method for the optimum design of structures made of an elasto-plastic material within the Hencky-Nadai-Ilyushin theory. This method provides the optimal layouts of the moduli of isotropy to make the overall compliance minimal. Th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Materials |
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| Online Access: | https://www.mdpi.com/1996-1944/14/23/7430 |
| _version_ | 1797507522918088704 |
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| author | Sławomir Czarnecki Tomasz Lewiński |
| author_facet | Sławomir Czarnecki Tomasz Lewiński |
| author_sort | Sławomir Czarnecki |
| collection | DOAJ |
| description | This paper puts forward a new version of the Isotropic Material Design method for the optimum design of structures made of an elasto-plastic material within the Hencky-Nadai-Ilyushin theory. This method provides the optimal layouts of the moduli of isotropy to make the overall compliance minimal. Thus, the bulk and shear moduli are the only design variables, both assumed as non-negative fields. The trace of the Hooke tensor represents the unit cost of the design. The yield condition is assumed to be independent of the design variables, to make the design process as simple as possible. By eliminating the design variables, the optimum design problem is reduced to the pair of the two mutually dual Linear Constrained Problems (LCP). The solution to the LCP stress-based problem directly determines the layout of the optimal moduli. A numerical method has been developed to construct approximate solutions, which paves the way for constructing the final layouts of the elastic moduli. Selected illustrative solutions are reported, corresponding to various data concerning the yield limit and the cost of the design. The yield condition introduced in this paper results in bounding the values of the optimal moduli in the places of possible stress concentration, such as reentrant corners. |
| first_indexed | 2024-03-10T04:49:39Z |
| format | Article |
| id | doaj.art-b4cfbc42e13e403eaec6ffb98f50c8ca |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-10T04:49:39Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Materials |
| spelling | doaj.art-b4cfbc42e13e403eaec6ffb98f50c8ca2023-11-23T02:43:24ZengMDPI AGMaterials1996-19442021-12-011423743010.3390/ma14237430The Isotropic Material Design of In-Plane Loaded Elasto-Plastic PlatesSławomir Czarnecki0Tomasz Lewiński1Faculty of Civil Engineering, Warsaw University of Technology, 00-637 Warszawa, PolandFaculty of Civil Engineering, Warsaw University of Technology, 00-637 Warszawa, PolandThis paper puts forward a new version of the Isotropic Material Design method for the optimum design of structures made of an elasto-plastic material within the Hencky-Nadai-Ilyushin theory. This method provides the optimal layouts of the moduli of isotropy to make the overall compliance minimal. Thus, the bulk and shear moduli are the only design variables, both assumed as non-negative fields. The trace of the Hooke tensor represents the unit cost of the design. The yield condition is assumed to be independent of the design variables, to make the design process as simple as possible. By eliminating the design variables, the optimum design problem is reduced to the pair of the two mutually dual Linear Constrained Problems (LCP). The solution to the LCP stress-based problem directly determines the layout of the optimal moduli. A numerical method has been developed to construct approximate solutions, which paves the way for constructing the final layouts of the elastic moduli. Selected illustrative solutions are reported, corresponding to various data concerning the yield limit and the cost of the design. The yield condition introduced in this paper results in bounding the values of the optimal moduli in the places of possible stress concentration, such as reentrant corners.https://www.mdpi.com/1996-1944/14/23/7430isotropic material designcompliance minimizationHencky-Nadai-Ilyushin plasticity |
| spellingShingle | Sławomir Czarnecki Tomasz Lewiński The Isotropic Material Design of In-Plane Loaded Elasto-Plastic Plates Materials isotropic material design compliance minimization Hencky-Nadai-Ilyushin plasticity |
| title | The Isotropic Material Design of In-Plane Loaded Elasto-Plastic Plates |
| title_full | The Isotropic Material Design of In-Plane Loaded Elasto-Plastic Plates |
| title_fullStr | The Isotropic Material Design of In-Plane Loaded Elasto-Plastic Plates |
| title_full_unstemmed | The Isotropic Material Design of In-Plane Loaded Elasto-Plastic Plates |
| title_short | The Isotropic Material Design of In-Plane Loaded Elasto-Plastic Plates |
| title_sort | isotropic material design of in plane loaded elasto plastic plates |
| topic | isotropic material design compliance minimization Hencky-Nadai-Ilyushin plasticity |
| url | https://www.mdpi.com/1996-1944/14/23/7430 |
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