1D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITY
We present a modified strain gradient theory of elasticity for linear isotropic materials in order to account for the so-called size effect. Additional material length scale parameters are introduced and the problem of static beam bending is analyzed. A numerical solution is derived by means of a fi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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CTU Central Library
2016-12-01
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| Series: | Acta Polytechnica CTU Proceedings |
| Online Access: | https://ojs.cvut.cz/ojs/index.php/APP/article/view/3959 |
| _version_ | 1811304916877049856 |
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| author | Christian Liebold Wolfgang H. Müller |
| author_facet | Christian Liebold Wolfgang H. Müller |
| author_sort | Christian Liebold |
| collection | DOAJ |
| description | We present a modified strain gradient theory of elasticity for linear isotropic materials in order to account for the so-called size effect. Additional material length scale parameters are introduced and the problem of static beam bending is analyzed. A numerical solution is derived by means of a finite element approach. A global C1-continuous displacement field is applied in finite element solutions because the higher-order strain energy density additionally depends on second gradients of displacements. So-called Hermite finite elements are used that allow for merging gradients between elements. The element stiffness matrix as well as the global stiffness matrix of the problem is developed. Convergence, C1-continuity and the size effect in the numerical solution is shown. Experiments on bending stiffnesses of different sized micro beams made of the polymer SU-8 are performed by using an atomic force microscope and the results are compared to the numerical solution. |
| first_indexed | 2024-04-13T08:15:58Z |
| format | Article |
| id | doaj.art-a1f6b9c3750d4efc99db99351f0a91de |
| institution | Directory Open Access Journal |
| issn | 2336-5382 |
| language | English |
| last_indexed | 2024-04-13T08:15:58Z |
| publishDate | 2016-12-01 |
| publisher | CTU Central Library |
| record_format | Article |
| series | Acta Polytechnica CTU Proceedings |
| spelling | doaj.art-a1f6b9c3750d4efc99db99351f0a91de2022-12-22T02:54:48ZengCTU Central LibraryActa Polytechnica CTU Proceedings2336-53822016-12-0170333710.14311/APP.2017.7.003334951D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITYChristian Liebold0Wolfgang H. Müller1Berlin University of Technology, Chair of Continuum Mechanics and Materials Theory, Einsteinufer 5, 10587 Berlin, GermanyBerlin University of Technology, Chair of Continuum Mechanics and Materials Theory, Einsteinufer 5, 10587 Berlin, GermanyWe present a modified strain gradient theory of elasticity for linear isotropic materials in order to account for the so-called size effect. Additional material length scale parameters are introduced and the problem of static beam bending is analyzed. A numerical solution is derived by means of a finite element approach. A global C1-continuous displacement field is applied in finite element solutions because the higher-order strain energy density additionally depends on second gradients of displacements. So-called Hermite finite elements are used that allow for merging gradients between elements. The element stiffness matrix as well as the global stiffness matrix of the problem is developed. Convergence, C1-continuity and the size effect in the numerical solution is shown. Experiments on bending stiffnesses of different sized micro beams made of the polymer SU-8 are performed by using an atomic force microscope and the results are compared to the numerical solution.https://ojs.cvut.cz/ojs/index.php/APP/article/view/3959 |
| spellingShingle | Christian Liebold Wolfgang H. Müller 1D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITY Acta Polytechnica CTU Proceedings |
| title | 1D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITY |
| title_full | 1D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITY |
| title_fullStr | 1D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITY |
| title_full_unstemmed | 1D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITY |
| title_short | 1D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITY |
| title_sort | 1d hermite elements for c1 continuous solutions in second gradient elasticity |
| url | https://ojs.cvut.cz/ojs/index.php/APP/article/view/3959 |
| work_keys_str_mv | AT christianliebold 1dhermiteelementsforc1continuoussolutionsinsecondgradientelasticity AT wolfganghmuller 1dhermiteelementsforc1continuoussolutionsinsecondgradientelasticity |