The Neumann–Monte Carlo methodology applied to the quantification of uncertainty in the problem stochastic bending of the Levinson–Bickford beam.
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| Title: | The Neumann–Monte Carlo methodology applied to the quantification of uncertainty in the problem stochastic bending of the Levinson–Bickford beam. |
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| Authors: | da S. Jr., Claudio R. Ávila1 (AUTHOR) avila@utfpr.edu.br, Squarcio, Roberto M. F.1 (AUTHOR) |
| Source: | Archive of Applied Mechanics. May2023, Vol. 93 Issue 5, p2009-2024. 16p. |
| Subjects: | Monte Carlo method, Predicate calculus, Stochastic processes |
| Abstract: | This paper proposes to apply the Neumann–Monte Carlo method to obtain the estimates of the statistical moments of the solution for the stochastic bending problem of Levinson–Bickford beams, with uncertainty in beam stiffness. The approximate solutions represent the stochastic displacement processes. For uncertainty modeling, parameterized stochastic processes will be used. The methodology proposed in this work differs from the usual one, as it is developed from theoretical results of existence and uniqueness of the realizations. The consistency of the approximate solutions will be based on studies on the existence and uniqueness of the theoretical solutions to this problem. The uncertainty will be quantified by estimating the statistical moments of the stochastic transverse displacement processes. The Monte Carlo simulation method is used to evaluate the performance of the proposed methodology and, for the numerical examples presented errors were obtained in the approximations of statistical estimators below 1%, and computation times were substantially reduced. [ABSTRACT FROM AUTHOR] |
| Copyright of Archive of Applied Mechanics 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: 163022832 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The Neumann–Monte Carlo methodology applied to the quantification of uncertainty in the problem stochastic bending of the Levinson–Bickford beam. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22da+S%2E+Jr%2E%2C+Claudio+R%2E+Ávila%22">da S. Jr., Claudio R. Ávila</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> avila@utfpr.edu.br</i><br /><searchLink fieldCode="AR" term="%22Squarcio%2C+Roberto+M%2E+F%2E%22">Squarcio, Roberto M. F.</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Archive+of+Applied+Mechanics%22">Archive of Applied Mechanics</searchLink>. May2023, Vol. 93 Issue 5, p2009-2024. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br /><searchLink fieldCode="DE" term="%22Predicate+calculus%22">Predicate calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper proposes to apply the Neumann–Monte Carlo method to obtain the estimates of the statistical moments of the solution for the stochastic bending problem of Levinson–Bickford beams, with uncertainty in beam stiffness. The approximate solutions represent the stochastic displacement processes. For uncertainty modeling, parameterized stochastic processes will be used. The methodology proposed in this work differs from the usual one, as it is developed from theoretical results of existence and uniqueness of the realizations. The consistency of the approximate solutions will be based on studies on the existence and uniqueness of the theoretical solutions to this problem. The uncertainty will be quantified by estimating the statistical moments of the stochastic transverse displacement processes. The Monte Carlo simulation method is used to evaluate the performance of the proposed methodology and, for the numerical examples presented errors were obtained in the approximations of statistical estimators below 1%, and computation times were substantially reduced. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Archive of Applied Mechanics 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/s00419-023-02369-5 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 2009 Subjects: – SubjectFull: Monte Carlo method Type: general – SubjectFull: Predicate calculus Type: general – SubjectFull: Stochastic processes Type: general Titles: – TitleFull: The Neumann–Monte Carlo methodology applied to the quantification of uncertainty in the problem stochastic bending of the Levinson–Bickford beam. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: da S. Jr., Claudio R. Ávila – PersonEntity: Name: NameFull: Squarcio, Roberto M. F. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 09391533 Numbering: – Type: volume Value: 93 – Type: issue Value: 5 Titles: – TitleFull: Archive of Applied Mechanics Type: main |
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