On variational aspects of a generalized continuum
The intention of the paper is to sketch the background of the Finsler bundle approach to the continuum theory of solids using variational arguments. Within this approach the additive decomposition of the total deformation gradient is defined. For a given Lagrangian function and an assumed one-param...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
1996-05-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
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| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1996(2)/315-327.pdf |
| _version_ | 1797821734998507520 |
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| author | J. SACZUK |
| author_facet | J. SACZUK |
| author_sort | J. SACZUK |
| collection | DOAJ |
| description | The intention of the paper is to sketch the background of the Finsler
bundle approach to the continuum theory of solids using variational arguments. Within this approach the additive decomposition of the total deformation gradient is defined. For a given Lagrangian function and an assumed one-parameter family of transformations of dependent and independent variables, the fundamental variational formula identified with the virtual work principle of the generalized (microstructural) continuum is obtained. Stationarity conditions of the action integral lead to the balance equations and natural boundary conditions valid on both the base space and the fibre space of the body.
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| first_indexed | 2024-03-13T09:58:11Z |
| format | Article |
| id | doaj.art-f16fcf1a8ea34e3fa2180b05a4beef49 |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-03-13T09:58:11Z |
| publishDate | 1996-05-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-f16fcf1a8ea34e3fa2180b05a4beef492023-05-23T15:21:08ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33501996-05-01162315327On variational aspects of a generalized continuumJ. SACZUK 0Institute of Fluid-Flow Machinery of the Polish Academy of Sciences – ul. J. Fiszera 14 – Pl-80-952 – Gda´nsk – PolandThe intention of the paper is to sketch the background of the Finsler bundle approach to the continuum theory of solids using variational arguments. Within this approach the additive decomposition of the total deformation gradient is defined. For a given Lagrangian function and an assumed one-parameter family of transformations of dependent and independent variables, the fundamental variational formula identified with the virtual work principle of the generalized (microstructural) continuum is obtained. Stationarity conditions of the action integral lead to the balance equations and natural boundary conditions valid on both the base space and the fibre space of the body. https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1996(2)/315-327.pdffinsler geometrycontinuum with microstructurevariational formulation |
| spellingShingle | J. SACZUK On variational aspects of a generalized continuum Rendiconti di Matematica e delle Sue Applicazioni finsler geometry continuum with microstructure variational formulation |
| title | On variational aspects of a generalized continuum |
| title_full | On variational aspects of a generalized continuum |
| title_fullStr | On variational aspects of a generalized continuum |
| title_full_unstemmed | On variational aspects of a generalized continuum |
| title_short | On variational aspects of a generalized continuum |
| title_sort | on variational aspects of a generalized continuum |
| topic | finsler geometry continuum with microstructure variational formulation |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1996(2)/315-327.pdf |
| work_keys_str_mv | AT jsaczuk onvariationalaspectsofageneralizedcontinuum |