Stress–displacement stabilized finite element analysis of thin structures using solid-shell elements, Part I: On the need of interpolating the stresses.
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| Title: | Stress–displacement stabilized finite element analysis of thin structures using solid-shell elements, Part I: On the need of interpolating the stresses. |
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| Authors: | Aguirre, A.1,2 (AUTHOR) alejandro.aguirre@upc.edu, Codina, R.1 (AUTHOR) ramon.codina@upc.edu, Baiges, J.1 (AUTHOR) joan.baiges@upc.edu |
| Source: | Finite Elements in Analysis & Design. Sep2024, Vol. 236, pN.PAG-N.PAG. 1p. |
| Subjects: | Finite element method, Strains & stresses (Mechanics), Curvilinear coordinates, Benchmark problems (Computer science) |
| Abstract: | This work studies the solid-shell finite element approach to approximate thin structures using a stabilized mixed displacement–stress formulation based on the Variational Multiscale framework. The work is divided in two parts. In Part I, the numerical locking effects inherent to the solid-shell approach are characterized using a variety of benchmark problems in the infinitesimal strain approximation. In Part II, the results are extended to formulate the mixed approach in finite strain hyperelastic problems. In the present work, the stabilized mixed displacement–stress formulation is proven to be adequate to deal with all kinds of numerical locking. Additionally, a more comprehensive analysis of each individual type of numerical locking, how it is triggered and how it is overcome is also provided. The numerical locking usually occurs when parasitic strains overtake the system of equations through specific components of the stress tensor. To properly analyze them, the direction of each component of the stress tensor has been defined with respect to the shell directors. Therefore, it becomes necessary to formulate the solid-shell problem in curvilinear coordinates, allowing to give mechanical meaning to the stress components (shear, twisting, membrane and thickness stresses) independently of the global frame of reference. The conditions in which numerical locking is triggered as well as the stress tensor component responsible of correcting the locking behavior have been identified individually by characterizing the numerical response of a set of different benchmark problems. • Stabilized finite element models for mixed displacement–stress models. • The effect of each stress component in curvilinear coordinates is studied. • A general methodology for the solid-shell representation is presented. • It is concluded that all components of stress are needed to avoid locking. • The final formulation is accurate and robust. [ABSTRACT FROM AUTHOR] |
| Copyright of Finite Elements in Analysis & Design 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: 177420113 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Stress–displacement stabilized finite element analysis of thin structures using solid-shell elements, Part I: On the need of interpolating the stresses. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Aguirre%2C+A%2E%22">Aguirre, A.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> alejandro.aguirre@upc.edu</i><br /><searchLink fieldCode="AR" term="%22Codina%2C+R%2E%22">Codina, R.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ramon.codina@upc.edu</i><br /><searchLink fieldCode="AR" term="%22Baiges%2C+J%2E%22">Baiges, J.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> joan.baiges@upc.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Finite+Elements+in+Analysis+%26+Design%22">Finite Elements in Analysis & Design</searchLink>. Sep2024, Vol. 236, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Strains+%26+stresses+%28Mechanics%29%22">Strains & stresses (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Curvilinear+coordinates%22">Curvilinear coordinates</searchLink><br /><searchLink fieldCode="DE" term="%22Benchmark+problems+%28Computer+science%29%22">Benchmark problems (Computer science)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This work studies the solid-shell finite element approach to approximate thin structures using a stabilized mixed displacement–stress formulation based on the Variational Multiscale framework. The work is divided in two parts. In Part I, the numerical locking effects inherent to the solid-shell approach are characterized using a variety of benchmark problems in the infinitesimal strain approximation. In Part II, the results are extended to formulate the mixed approach in finite strain hyperelastic problems. In the present work, the stabilized mixed displacement–stress formulation is proven to be adequate to deal with all kinds of numerical locking. Additionally, a more comprehensive analysis of each individual type of numerical locking, how it is triggered and how it is overcome is also provided. The numerical locking usually occurs when parasitic strains overtake the system of equations through specific components of the stress tensor. To properly analyze them, the direction of each component of the stress tensor has been defined with respect to the shell directors. Therefore, it becomes necessary to formulate the solid-shell problem in curvilinear coordinates, allowing to give mechanical meaning to the stress components (shear, twisting, membrane and thickness stresses) independently of the global frame of reference. The conditions in which numerical locking is triggered as well as the stress tensor component responsible of correcting the locking behavior have been identified individually by characterizing the numerical response of a set of different benchmark problems. • Stabilized finite element models for mixed displacement–stress models. • The effect of each stress component in curvilinear coordinates is studied. • A general methodology for the solid-shell representation is presented. • It is concluded that all components of stress are needed to avoid locking. • The final formulation is accurate and robust. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Finite Elements in Analysis & Design 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.finel.2024.104168 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Finite element method Type: general – SubjectFull: Strains & stresses (Mechanics) Type: general – SubjectFull: Curvilinear coordinates Type: general – SubjectFull: Benchmark problems (Computer science) Type: general Titles: – TitleFull: Stress–displacement stabilized finite element analysis of thin structures using solid-shell elements, Part I: On the need of interpolating the stresses. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Aguirre, A. – PersonEntity: Name: NameFull: Codina, R. – PersonEntity: Name: NameFull: Baiges, J. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 0168874X Numbering: – Type: volume Value: 236 Titles: – TitleFull: Finite Elements in Analysis & Design Type: main |
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