Two-Scale Finite Element Approximation of a Homogenized Plate Model
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909226573496320 |
|---|---|
| author | Rumpf, Martin Simon, Stefan Smoch, Christoph |
| author_facet | Rumpf, Martin Simon, Stefan Smoch, Christoph |
| contents | This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Velčić in 2014. Thereby, a nonlinear bending energy is based on a homogenized quadratic form which acts on the second fundamental form associated with the elastic deformation. Convergence is proven for a multi-affine finite element discretization of the involved three-dimensional microscopic cell problems and a discrete Kirchhoff triangle discretization of the two-dimensional isometry-constrained macroscopic problem. Finally, the convergence properties are numerically verified in selected test cases and qualitatively compared with deformation experiments for microstructured sheets of paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14431 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two-Scale Finite Element Approximation of a Homogenized Plate Model Rumpf, Martin Simon, Stefan Smoch, Christoph Numerical Analysis 65N12, 65N30, 74E25, 74K20 This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Velčić in 2014. Thereby, a nonlinear bending energy is based on a homogenized quadratic form which acts on the second fundamental form associated with the elastic deformation. Convergence is proven for a multi-affine finite element discretization of the involved three-dimensional microscopic cell problems and a discrete Kirchhoff triangle discretization of the two-dimensional isometry-constrained macroscopic problem. Finally, the convergence properties are numerically verified in selected test cases and qualitatively compared with deformation experiments for microstructured sheets of paper. |
| title | Two-Scale Finite Element Approximation of a Homogenized Plate Model |
| topic | Numerical Analysis 65N12, 65N30, 74E25, 74K20 |
| url | https://arxiv.org/abs/2308.14431 |