Approximating the inertia forces in the floating frame of reference formulation using the consistent finite element mass matrix: Approximating the inertia forces in the floating frame: K. van Voorthuizen et al.
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| Title: | Approximating the inertia forces in the floating frame of reference formulation using the consistent finite element mass matrix: Approximating the inertia forces in the floating frame: K. van Voorthuizen et al. |
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| Authors: | van Voorthuizen, Karlijn1 (AUTHOR) k.l.vanvoorthuizen@utwente.nl, Abdul Rasheed, Mohammed Iqbal1 (AUTHOR) m.i.abdulrasheed@utwente.nl, Schilder, Jurnan1 (AUTHOR) j.p.schilder@utwente.nl, Ellenbroek, Marcel1 (AUTHOR) m.h.m.ellenbroek@utwente.nl |
| Source: | Acta Mechanica. Mar2025, Vol. 236 Issue 3, p1955-1976. 22p. |
| Subjects: | Finite element method, Lumped elements, Equations of motion, Kinetic energy, Energy consumption |
| Abstract: | In the floating frame of reference formulation, the exact form of the inertia forces is derived using a continuum-based approach. This yields a mass matrix and quadratic velocity terms containing inertia shape integrals. To avoid these integrals, many implementations of the floating frame formulation approximate the inertia forces by defining the kinetic energy using the lumped finite element mass matrix. This work proposes an alternative approximation of the inertia forces based on the consistent finite element mass matrix for structural elements, addressing cases where the exact solutions available in literature for most solid elements are not applicable. The inertia forces are derived by defining the kinetic energy using the consistent finite element mass matrix or by using the inertia forces from the equation of motion of the corresponding linear finite element model. In this way, the inertia shape integrals are replaced by a readily available mass matrix. In comparison with the lumped approach, the proposed definition yields more accurate results for coarser meshes since a more realistic representation of the mass and inertia properties of the body is used. Furthermore, the proposed approach yields inertia forces similar to the exact continuum-based approach under the assumption of small deformations. If the influence of deformation on the mass matrix is significant or the quadratic velocity terms are important, mesh refinement is required to accurately represent the inertia forces. The accuracy of the proposed definition of the inertia forces is compared to the exact and lumped mass approaches through simulation of flexible systems. [ABSTRACT FROM AUTHOR] |
| Copyright of Acta Mechanica is the property of Springer Nature 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 183750935 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Approximating the inertia forces in the floating frame of reference formulation using the consistent finite element mass matrix: Approximating the inertia forces in the floating frame: K. van Voorthuizen et al. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22van+Voorthuizen%2C+Karlijn%22">van Voorthuizen, Karlijn</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> k.l.vanvoorthuizen@utwente.nl</i><br /><searchLink fieldCode="AR" term="%22Abdul+Rasheed%2C+Mohammed+Iqbal%22">Abdul Rasheed, Mohammed Iqbal</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> m.i.abdulrasheed@utwente.nl</i><br /><searchLink fieldCode="AR" term="%22Schilder%2C+Jurnan%22">Schilder, Jurnan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> j.p.schilder@utwente.nl</i><br /><searchLink fieldCode="AR" term="%22Ellenbroek%2C+Marcel%22">Ellenbroek, Marcel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> m.h.m.ellenbroek@utwente.nl</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Acta+Mechanica%22">Acta Mechanica</searchLink>. Mar2025, Vol. 236 Issue 3, p1955-1976. 22p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Lumped+elements%22">Lumped elements</searchLink><br /><searchLink fieldCode="DE" term="%22Equations+of+motion%22">Equations of motion</searchLink><br /><searchLink fieldCode="DE" term="%22Kinetic+energy%22">Kinetic energy</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+consumption%22">Energy consumption</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In the floating frame of reference formulation, the exact form of the inertia forces is derived using a continuum-based approach. This yields a mass matrix and quadratic velocity terms containing inertia shape integrals. To avoid these integrals, many implementations of the floating frame formulation approximate the inertia forces by defining the kinetic energy using the lumped finite element mass matrix. This work proposes an alternative approximation of the inertia forces based on the consistent finite element mass matrix for structural elements, addressing cases where the exact solutions available in literature for most solid elements are not applicable. The inertia forces are derived by defining the kinetic energy using the consistent finite element mass matrix or by using the inertia forces from the equation of motion of the corresponding linear finite element model. In this way, the inertia shape integrals are replaced by a readily available mass matrix. In comparison with the lumped approach, the proposed definition yields more accurate results for coarser meshes since a more realistic representation of the mass and inertia properties of the body is used. Furthermore, the proposed approach yields inertia forces similar to the exact continuum-based approach under the assumption of small deformations. If the influence of deformation on the mass matrix is significant or the quadratic velocity terms are important, mesh refinement is required to accurately represent the inertia forces. The accuracy of the proposed definition of the inertia forces is compared to the exact and lumped mass approaches through simulation of flexible systems. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Acta Mechanica is the property of Springer Nature 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: 10.1007/s00707-025-04247-3 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 1955 Subjects: – SubjectFull: Finite element method Type: general – SubjectFull: Lumped elements Type: general – SubjectFull: Equations of motion Type: general – SubjectFull: Kinetic energy Type: general – SubjectFull: Energy consumption Type: general Titles: – TitleFull: Approximating the inertia forces in the floating frame of reference formulation using the consistent finite element mass matrix: Approximating the inertia forces in the floating frame: K. van Voorthuizen et al. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: van Voorthuizen, Karlijn – PersonEntity: Name: NameFull: Abdul Rasheed, Mohammed Iqbal – PersonEntity: Name: NameFull: Schilder, Jurnan – PersonEntity: Name: NameFull: Ellenbroek, Marcel IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00015970 Numbering: – Type: volume Value: 236 – Type: issue Value: 3 Titles: – TitleFull: Acta Mechanica Type: main |
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