Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives
This study extends the functional interpolation framework, introduced by the Theory of Functional Connections, initially introduced for functions, derivatives, integrals, components, and any linear combination of them, to constraints made of shear-type and/or mixed derivatives. The main motivation c...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/24/4692 |
| _version_ | 1797456447513034752 |
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| author | Daniele Mortari |
| author_facet | Daniele Mortari |
| author_sort | Daniele Mortari |
| collection | DOAJ |
| description | This study extends the functional interpolation framework, introduced by the Theory of Functional Connections, initially introduced for functions, derivatives, integrals, components, and any linear combination of them, to constraints made of shear-type and/or mixed derivatives. The main motivation comes from differential equations, often appearing in fluid dynamics and structures/materials problems that are subject to shear-type and/or mixed boundary derivatives constraints. This is performed by replacing these boundary constraints with equivalent constraints, obtained using indefinite integrals. In addition, this study also shows how to validate the constraints’ consistency when the problem involves the unknown constants of integrations generated by indefinite integrations. |
| first_indexed | 2024-03-09T16:07:58Z |
| format | Article |
| id | doaj.art-43d016474a914135acf525f325553dc0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:07:58Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-43d016474a914135acf525f325553dc02023-11-24T16:28:04ZengMDPI AGMathematics2227-73902022-12-011024469210.3390/math10244692Theory of Functional Connections Subject to Shear-Type and Mixed DerivativesDaniele Mortari0Aerospace Engineering, Texas A&M University, 3141 TAMU, College Station, TX 77843, USAThis study extends the functional interpolation framework, introduced by the Theory of Functional Connections, initially introduced for functions, derivatives, integrals, components, and any linear combination of them, to constraints made of shear-type and/or mixed derivatives. The main motivation comes from differential equations, often appearing in fluid dynamics and structures/materials problems that are subject to shear-type and/or mixed boundary derivatives constraints. This is performed by replacing these boundary constraints with equivalent constraints, obtained using indefinite integrals. In addition, this study also shows how to validate the constraints’ consistency when the problem involves the unknown constants of integrations generated by indefinite integrations.https://www.mdpi.com/2227-7390/10/24/4692functional interpolationdifferential equationsnumerical methods |
| spellingShingle | Daniele Mortari Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives Mathematics functional interpolation differential equations numerical methods |
| title | Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives |
| title_full | Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives |
| title_fullStr | Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives |
| title_full_unstemmed | Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives |
| title_short | Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives |
| title_sort | theory of functional connections subject to shear type and mixed derivatives |
| topic | functional interpolation differential equations numerical methods |
| url | https://www.mdpi.com/2227-7390/10/24/4692 |
| work_keys_str_mv | AT danielemortari theoryoffunctionalconnectionssubjecttosheartypeandmixedderivatives |