A Reissner–Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations.
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| Title: | A Reissner–Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations. |
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| Authors: | Sky, Adam1 (AUTHOR) adam.sky@uni.lu, Neunteufel, Michael2 (AUTHOR) michael.neunteufel@tuwien.ac.at, Hale, Jack S.1 (AUTHOR) jack.hale@uni.lu, Zilian, Andreas1 (AUTHOR) andreas.zilian@uni.lu |
| Source: | Computer Methods in Applied Mechanics & Engineering. Nov2023, Vol. 416, pN.PAG-N.PAG. 1p. |
| Subjects: | Bending moment, Shearing force, Symmetric spaces, Iron & steel plates |
| Abstract: | In this work we develop new finite element discretisations of the shear-deformable Reissner–Mindlin plate problem based on the Hellinger–Reissner principle of symmetric stresses. Specifically, we use conforming Hu-Zhang elements to discretise the bending moments in the space of symmetric square integrable fields with a square integrable divergence M ∈ HZ ⊂ H sym (Div). The latter results in highly accurate approximations of the bending moments M and in the rotation field being in the Lebesgue space ϕ ∈ [ L 2 ] 2 , such that the Kirchhoff–Love constraint can be satisfied for t → 0. In order to preserve optimal convergence rates across all variables for the case t → 0 , we present an extension of the formulation using Raviart–Thomas elements for the shear stress q ∈ RT ⊂ H (div). We prove existence and uniqueness in the continuous setting and rely on exact complexes for inheritance of well-posedness in the discrete setting. This work introduces an efficient construction of the Hu-Zhang base functions on the reference element via the polytopal template methodology and Legendre polynomials, making it applicable to hp-FEM. The base functions on the reference element are then mapped to the physical element using novel polytopal transformations, which are suitable also for curved geometries. The robustness of the formulations and the construction of the Hu-Zhang element are tested for shear-locking, curved geometries and an L-shaped domain with a singularity in the bending moments M. Further, we compare the performance of the novel formulations with the primal-, MITC- and recently introduced TDNNS methods. • Novel variational formulations of the Reissner-Mindlin plate via Hu-Zhang elements. • Well-posedness proofs, robustness proofs, and a priori error estimates. • New formulas for the Hu-Zhang basis via polytopal templates and Legendre polynomials. • Novel mappings of the base functions from the reference- to the physical element. • Techniques for the embedding of Dirichlet boundary conditions in the Hu-Zhang space. [ABSTRACT FROM AUTHOR] |
| Copyright of Computer Methods in Applied Mechanics & Engineering is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 173278005 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Reissner–Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Sky%2C+Adam%22">Sky, Adam</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> adam.sky@uni.lu</i><br /><searchLink fieldCode="AR" term="%22Neunteufel%2C+Michael%22">Neunteufel, Michael</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> michael.neunteufel@tuwien.ac.at</i><br /><searchLink fieldCode="AR" term="%22Hale%2C+Jack+S%2E%22">Hale, Jack S.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jack.hale@uni.lu</i><br /><searchLink fieldCode="AR" term="%22Zilian%2C+Andreas%22">Zilian, Andreas</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> andreas.zilian@uni.lu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computer+Methods+in+Applied+Mechanics+%26+Engineering%22">Computer Methods in Applied Mechanics & Engineering</searchLink>. Nov2023, Vol. 416, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Bending+moment%22">Bending moment</searchLink><br /><searchLink fieldCode="DE" term="%22Shearing+force%22">Shearing force</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetric+spaces%22">Symmetric spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Iron+%26+steel+plates%22">Iron & steel plates</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this work we develop new finite element discretisations of the shear-deformable Reissner–Mindlin plate problem based on the Hellinger–Reissner principle of symmetric stresses. Specifically, we use conforming Hu-Zhang elements to discretise the bending moments in the space of symmetric square integrable fields with a square integrable divergence M ∈ HZ ⊂ H sym (Div). The latter results in highly accurate approximations of the bending moments M and in the rotation field being in the Lebesgue space ϕ ∈ [ L 2 ] 2 , such that the Kirchhoff–Love constraint can be satisfied for t → 0. In order to preserve optimal convergence rates across all variables for the case t → 0 , we present an extension of the formulation using Raviart–Thomas elements for the shear stress q ∈ RT ⊂ H (div). We prove existence and uniqueness in the continuous setting and rely on exact complexes for inheritance of well-posedness in the discrete setting. This work introduces an efficient construction of the Hu-Zhang base functions on the reference element via the polytopal template methodology and Legendre polynomials, making it applicable to hp-FEM. The base functions on the reference element are then mapped to the physical element using novel polytopal transformations, which are suitable also for curved geometries. The robustness of the formulations and the construction of the Hu-Zhang element are tested for shear-locking, curved geometries and an L-shaped domain with a singularity in the bending moments M. Further, we compare the performance of the novel formulations with the primal-, MITC- and recently introduced TDNNS methods. • Novel variational formulations of the Reissner-Mindlin plate via Hu-Zhang elements. • Well-posedness proofs, robustness proofs, and a priori error estimates. • New formulas for the Hu-Zhang basis via polytopal templates and Legendre polynomials. • Novel mappings of the base functions from the reference- to the physical element. • Techniques for the embedding of Dirichlet boundary conditions in the Hu-Zhang space. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Computer Methods in Applied Mechanics & Engineering is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.cma.2023.116291 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Bending moment Type: general – SubjectFull: Shearing force Type: general – SubjectFull: Symmetric spaces Type: general – SubjectFull: Iron & steel plates Type: general Titles: – TitleFull: A Reissner–Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Sky, Adam – PersonEntity: Name: NameFull: Neunteufel, Michael – PersonEntity: Name: NameFull: Hale, Jack S. – PersonEntity: Name: NameFull: Zilian, Andreas IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 00457825 Numbering: – Type: volume Value: 416 Titles: – TitleFull: Computer Methods in Applied Mechanics & Engineering Type: main |
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