Integration of Direction Fields with Standard Options in Finite Element Programs
The two-dimensional differential equation y’ = f(x,y) can be interpreted as a direction field. Commercial Finite Element (FE) programs can be used for this integration task without additional programming, provided that these programs have options for the calculation of orthotropic heat conduction pr...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-05-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | http://www.mdpi.com/2297-8747/23/2/24 |
| _version_ | 1819030532990697472 |
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| author | Herbert Moldenhauer |
| author_facet | Herbert Moldenhauer |
| author_sort | Herbert Moldenhauer |
| collection | DOAJ |
| description | The two-dimensional differential equation y’ = f(x,y) can be interpreted as a direction field. Commercial Finite Element (FE) programs can be used for this integration task without additional programming, provided that these programs have options for the calculation of orthotropic heat conduction problems. The differential equation to be integrated with arbitrary boundaries is idealized as an FE model with thermal 2D elements. Its orthotropic thermal conductivities are specified as k1 = 1 and k2 = 0. In doing so, k1 is parallel to y´, and k2 is oriented perpendicular to this. For this extreme case, it is shown that the isotherms are identical to the solution of y’ = f(x,y). The direction fields, for example, can be velocity vectors in fluid mechanics or principal stress directions in structural mechanics. In the case of the latter, possibilities for application in the construction of fiber-reinforced plastics (FRP) arise, since fiber courses, which follow the local principal stress directions, make use of the superior stiffness and strength of the fibers. |
| first_indexed | 2024-12-21T06:31:40Z |
| format | Article |
| id | doaj.art-7126b175e8fd4a7c91fcf641bc2c8da0 |
| institution | Directory Open Access Journal |
| issn | 2297-8747 |
| language | English |
| last_indexed | 2024-12-21T06:31:40Z |
| publishDate | 2018-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-7126b175e8fd4a7c91fcf641bc2c8da02022-12-21T19:12:58ZengMDPI AGMathematical and Computational Applications2297-87472018-05-012322410.3390/mca23020024mca23020024Integration of Direction Fields with Standard Options in Finite Element ProgramsHerbert Moldenhauer0Dipl.-Ing. H. Moldenhauer GmbH, Im Brückengarten 9 A, 63322 Rödermark, GermanyThe two-dimensional differential equation y’ = f(x,y) can be interpreted as a direction field. Commercial Finite Element (FE) programs can be used for this integration task without additional programming, provided that these programs have options for the calculation of orthotropic heat conduction problems. The differential equation to be integrated with arbitrary boundaries is idealized as an FE model with thermal 2D elements. Its orthotropic thermal conductivities are specified as k1 = 1 and k2 = 0. In doing so, k1 is parallel to y´, and k2 is oriented perpendicular to this. For this extreme case, it is shown that the isotherms are identical to the solution of y’ = f(x,y). The direction fields, for example, can be velocity vectors in fluid mechanics or principal stress directions in structural mechanics. In the case of the latter, possibilities for application in the construction of fiber-reinforced plastics (FRP) arise, since fiber courses, which follow the local principal stress directions, make use of the superior stiffness and strength of the fibers.http://www.mdpi.com/2297-8747/23/2/24direction fieldtensor lineprincipal stresstailored fiber placementheat conduction |
| spellingShingle | Herbert Moldenhauer Integration of Direction Fields with Standard Options in Finite Element Programs Mathematical and Computational Applications direction field tensor line principal stress tailored fiber placement heat conduction |
| title | Integration of Direction Fields with Standard Options in Finite Element Programs |
| title_full | Integration of Direction Fields with Standard Options in Finite Element Programs |
| title_fullStr | Integration of Direction Fields with Standard Options in Finite Element Programs |
| title_full_unstemmed | Integration of Direction Fields with Standard Options in Finite Element Programs |
| title_short | Integration of Direction Fields with Standard Options in Finite Element Programs |
| title_sort | integration of direction fields with standard options in finite element programs |
| topic | direction field tensor line principal stress tailored fiber placement heat conduction |
| url | http://www.mdpi.com/2297-8747/23/2/24 |
| work_keys_str_mv | AT herbertmoldenhauer integrationofdirectionfieldswithstandardoptionsinfiniteelementprograms |