Simultaneous analysis of curved Kirchhoff beams and Kirchhoff--Love shells embedded in bulk domains
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910244276273152 |
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| author | Neumeyer, Jonas Kaiser, Michael Wolfgang Fries, Thomas-Peter |
| author_facet | Neumeyer, Jonas Kaiser, Michael Wolfgang Fries, Thomas-Peter |
| contents | A set of curved beams and shells is geometrically implied by level sets of a scalar function over some bulk domain. The mechanical model for each structure is based on the Kirchhoff--Love theory, that is, small displacements without shear deformations are considered. These models for individual geometries are extended to bulk models, simultaneously modeling the whole set of beams/shells on all level sets. A major focus is on the numerical analysis of such models. A mixed-hybrid and higher-order accurate Bulk Trace FEM is proposed that enables the use of standard $C^0$-continuous Lagrange elements with dimensionality of the bulk domain. That is, the higher-order continuity requirements of displacement-based formulations in context of the Kirchhoff--Love theory are successfully alleviated. Several numerical tests confirm the accuracy and higher-order convergence of the proposed methodology, also qualifying as benchmark test cases in future studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14566 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simultaneous analysis of curved Kirchhoff beams and Kirchhoff--Love shells embedded in bulk domains Neumeyer, Jonas Kaiser, Michael Wolfgang Fries, Thomas-Peter Computational Engineering, Finance, and Science A set of curved beams and shells is geometrically implied by level sets of a scalar function over some bulk domain. The mechanical model for each structure is based on the Kirchhoff--Love theory, that is, small displacements without shear deformations are considered. These models for individual geometries are extended to bulk models, simultaneously modeling the whole set of beams/shells on all level sets. A major focus is on the numerical analysis of such models. A mixed-hybrid and higher-order accurate Bulk Trace FEM is proposed that enables the use of standard $C^0$-continuous Lagrange elements with dimensionality of the bulk domain. That is, the higher-order continuity requirements of displacement-based formulations in context of the Kirchhoff--Love theory are successfully alleviated. Several numerical tests confirm the accuracy and higher-order convergence of the proposed methodology, also qualifying as benchmark test cases in future studies. |
| title | Simultaneous analysis of curved Kirchhoff beams and Kirchhoff--Love shells embedded in bulk domains |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2602.14566 |