A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates
The homogenization problem for a nonhornogeneous plate of doubly periodic structure is discussed. lt has been proved that an effective plate with constant effective homogenized stiffnesses is (in a certain meaning) energy equivalent to the considered heterogeneous plate of Y-periodic stiffnesses. M...
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| Format: | Article |
| Language: | English |
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Institute of Fundamental Technological Research
1986-09-01
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| Series: | Engineering Transactions |
| Online Access: | https://et.ippt.pan.pl/index.php/et/article/view/1815 |
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| author | T. Lewiński |
| author_facet | T. Lewiński |
| author_sort | T. Lewiński |
| collection | DOAJ |
| description |
The homogenization problem for a nonhornogeneous plate of doubly periodic structure is discussed. lt has been proved that an effective plate with constant effective homogenized stiffnesses is (in a certain meaning) energy equivalent to the considered heterogeneous plate of Y-periodic stiffnesses. Moreover, the corrector of the homogenized solution is defined and then its elementary derivation is presented, emphasis being put on the physical clearness of the procedure. In the last section a particular case of a plate with the thickness periodic in one (x1) direction is examined. A comparison is made of two sets of formulas for effective stiffnesses proposed by Duvaut and Kączkowski, respectively. lt is noted that the two formulae for D1212 and D2222 do not coincide.
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| format | Article |
| id | doaj-art-674ca8f6163545a1b8433f85ae3bf033 |
| institution | Kabale University |
| issn | 0867-888X 2450-8071 |
| language | English |
| publishDate | 1986-09-01 |
| publisher | Institute of Fundamental Technological Research |
| record_format | Article |
| series | Engineering Transactions |
| spelling | doaj-art-674ca8f6163545a1b8433f85ae3bf0332025-08-20T03:49:51ZengInstitute of Fundamental Technological ResearchEngineering Transactions0867-888X2450-80711986-09-01343A Note on Averaging of Stiffnesses of Thin Elastic Periodic PlatesT. Lewiński0Technical University of Warszawa, Warszawa The homogenization problem for a nonhornogeneous plate of doubly periodic structure is discussed. lt has been proved that an effective plate with constant effective homogenized stiffnesses is (in a certain meaning) energy equivalent to the considered heterogeneous plate of Y-periodic stiffnesses. Moreover, the corrector of the homogenized solution is defined and then its elementary derivation is presented, emphasis being put on the physical clearness of the procedure. In the last section a particular case of a plate with the thickness periodic in one (x1) direction is examined. A comparison is made of two sets of formulas for effective stiffnesses proposed by Duvaut and Kączkowski, respectively. lt is noted that the two formulae for D1212 and D2222 do not coincide. https://et.ippt.pan.pl/index.php/et/article/view/1815 |
| spellingShingle | T. Lewiński A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates Engineering Transactions |
| title | A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates |
| title_full | A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates |
| title_fullStr | A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates |
| title_full_unstemmed | A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates |
| title_short | A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates |
| title_sort | note on averaging of stiffnesses of thin elastic periodic plates |
| url | https://et.ippt.pan.pl/index.php/et/article/view/1815 |
| work_keys_str_mv | AT tlewinski anoteonaveragingofstiffnessesofthinelasticperiodicplates AT tlewinski noteonaveragingofstiffnessesofthinelasticperiodicplates |