Relative Entropy Computations for Nonlinear Deformations of the Porous Steel Structures.
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| Title: | Relative Entropy Computations for Nonlinear Deformations of the Porous Steel Structures. |
|---|---|
| Authors: | Strąkowski, Michał1 (AUTHOR), Kamiński, Marcin1 (AUTHOR) marcin.kaminski@p.lodz.pl |
| Source: | Materials (1996-1944). May2026, Vol. 19 Issue 9, p1783. 15p. |
| Subjects: | Structural reliability, Information measurement, Moments method (Statistics), Deformations (Mechanics), Damage models, Finite element method, Porous metals |
| Abstract: | In this paper, we investigate the application of the relative entropy framework for safety assessments of steel elements with structural defects at the micro- and macro-scales. Mathematical theories developed by Bhattacharyya and by Kullback and Leibler (K-L) have been used for this purpose. This approach uses both expectations and variations, similar to the First-Order Reliability Method (FORM), but is extended to include 3rd- and 4th-order central probabilistic moments. It is necessary to use a hybrid computational technique that combines the Finite Element Method (FEM) software ABAQUS CAE 2017 with the implemented Gurson–Tvergaard–Needleman (GTN) damage model and the computer algebra system MAPLE. The iterative generalized stochastic perturbation technique has been used to determine the probabilistic moments of structural response, to utilize the Weighted Least Squares Method to approximate the structural response function, and to determine uncertainty in the stress, strain, and displacement state functions. This approach is based on relative entropy because of its universality. There is no need to assume a type of distribution of the state functions, in contrast to FORM, where a Gaussian distribution is required. This paper verifies whether relative entropy can serve as an alternative to FORM for determining reliability. The yield surface of the porous material with a random values of the void volume fraction f are also presented. [ABSTRACT FROM AUTHOR] |
| Copyright of Materials (1996-1944) is the property of MDPI 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: 193715589 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Relative Entropy Computations for Nonlinear Deformations of the Porous Steel Structures. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Strąkowski%2C+Michał%22">Strąkowski, Michał</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Kamiński%2C+Marcin%22">Kamiński, Marcin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> marcin.kaminski@p.lodz.pl</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Materials+%281996-1944%29%22">Materials (1996-1944)</searchLink>. May2026, Vol. 19 Issue 9, p1783. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Structural+reliability%22">Structural reliability</searchLink><br /><searchLink fieldCode="DE" term="%22Information+measurement%22">Information measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Moments+method+%28Statistics%29%22">Moments method (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Deformations+%28Mechanics%29%22">Deformations (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Damage+models%22">Damage models</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Porous+metals%22">Porous metals</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we investigate the application of the relative entropy framework for safety assessments of steel elements with structural defects at the micro- and macro-scales. Mathematical theories developed by Bhattacharyya and by Kullback and Leibler (K-L) have been used for this purpose. This approach uses both expectations and variations, similar to the First-Order Reliability Method (FORM), but is extended to include 3rd- and 4th-order central probabilistic moments. It is necessary to use a hybrid computational technique that combines the Finite Element Method (FEM) software ABAQUS CAE 2017 with the implemented Gurson–Tvergaard–Needleman (GTN) damage model and the computer algebra system MAPLE. The iterative generalized stochastic perturbation technique has been used to determine the probabilistic moments of structural response, to utilize the Weighted Least Squares Method to approximate the structural response function, and to determine uncertainty in the stress, strain, and displacement state functions. This approach is based on relative entropy because of its universality. There is no need to assume a type of distribution of the state functions, in contrast to FORM, where a Gaussian distribution is required. This paper verifies whether relative entropy can serve as an alternative to FORM for determining reliability. The yield surface of the porous material with a random values of the void volume fraction f are also presented. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Materials (1996-1944) is the property of MDPI 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: 10.3390/ma19091783 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 1783 Subjects: – SubjectFull: Structural reliability Type: general – SubjectFull: Information measurement Type: general – SubjectFull: Moments method (Statistics) Type: general – SubjectFull: Deformations (Mechanics) Type: general – SubjectFull: Damage models Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Porous metals Type: general Titles: – TitleFull: Relative Entropy Computations for Nonlinear Deformations of the Porous Steel Structures. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Strąkowski, Michał – PersonEntity: Name: NameFull: Kamiński, Marcin IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 19961944 Numbering: – Type: volume Value: 19 – Type: issue Value: 9 Titles: – TitleFull: Materials (1996-1944) Type: main |
| ResultId | 1 |
