Academic Journal
A Mesh-Free Physics-Informed Neural Network Framework for Solving Plane Problems without Locking Issues.
| Τίτλος: | A Mesh-Free Physics-Informed Neural Network Framework for Solving Plane Problems without Locking Issues. |
|---|---|
| Συγγραφείς: | Lin, Zhipeng, Du, Ke, Li, Zepeng |
| Πηγή: | Journal of Applied & Computational Mechanics; Summer2026, Vol. 12 Issue 3, p1047-1068, 22p |
| Θεματικοί όροι: | Meshfree methods, Artificial neural networks, Partial differential equations, Finite element method, Strains & stresses (Mechanics) |
| Περίληψη: | This study proposes a plane problem solving method based on Physics-Informed Neural Network (PINN) for dealing with plane stress and strain problems, effectively avoiding the common shear locking and volume locking phenomena in traditional finite element methods, and exploring their underlying mechanisms. For the problem of plane stress, a PINN model based on strong form partial differential equations was constructed by randomly generating interior and boundary points within the solution domain, embedding the stress equilibrium equations and constitutive relations into the loss function. By minimizing the loss function, the network can automatically learn stress and displacement fields that satisfy the governing equations and boundary conditions. Numerical experiments show that this method can accurately predict stress distribution, effectively avoid shear locking, and maintain high accuracy even in thin plate structures. Further extension of the method to plane strain problems also successfully solved volume locking. This study also systematically compares two loss function construction methods based on strong form and energy principle (weak form). The results show that PINN, with its continuous and meshless solving characteristics, can fundamentally avoid the locking problem caused by low order element discretization, and both forms have high accuracy. This study validates the effectiveness and superiority of PINN in planar problems, providing new ideas and theoretical basis for overcoming traditional finite element locking problems. This method does not require complex element construction or numerical integration, and combines computational efficiency and accuracy, with good engineering application prospects. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Applied & Computational Mechanics is the property of Shahid Chamran University of Ahvaz 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.) | |
| Βάση Δεδομένων: | Complementary Index |
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| Items | – Name: Title Label: Title Group: Ti Data: A Mesh-Free Physics-Informed Neural Network Framework for Solving Plane Problems without Locking Issues. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Lin%2C+Zhipeng%22">Lin, Zhipeng</searchLink><br /><searchLink fieldCode="AR" term="%22Du%2C+Ke%22">Du, Ke</searchLink><br /><searchLink fieldCode="AR" term="%22Li%2C+Zepeng%22">Li, Zepeng</searchLink> – Name: TitleSource Label: Source Group: Src Data: Journal of Applied & Computational Mechanics; Summer2026, Vol. 12 Issue 3, p1047-1068, 22p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Meshfree+methods%22">Meshfree methods</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><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> – Name: Abstract Label: Abstract Group: Ab Data: This study proposes a plane problem solving method based on Physics-Informed Neural Network (PINN) for dealing with plane stress and strain problems, effectively avoiding the common shear locking and volume locking phenomena in traditional finite element methods, and exploring their underlying mechanisms. For the problem of plane stress, a PINN model based on strong form partial differential equations was constructed by randomly generating interior and boundary points within the solution domain, embedding the stress equilibrium equations and constitutive relations into the loss function. By minimizing the loss function, the network can automatically learn stress and displacement fields that satisfy the governing equations and boundary conditions. Numerical experiments show that this method can accurately predict stress distribution, effectively avoid shear locking, and maintain high accuracy even in thin plate structures. Further extension of the method to plane strain problems also successfully solved volume locking. This study also systematically compares two loss function construction methods based on strong form and energy principle (weak form). The results show that PINN, with its continuous and meshless solving characteristics, can fundamentally avoid the locking problem caused by low order element discretization, and both forms have high accuracy. This study validates the effectiveness and superiority of PINN in planar problems, providing new ideas and theoretical basis for overcoming traditional finite element locking problems. This method does not require complex element construction or numerical integration, and combines computational efficiency and accuracy, with good engineering application prospects. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Journal of Applied & Computational Mechanics is the property of Shahid Chamran University of Ahvaz 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: 10.22055/jacm.2025.48578.5339 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 1047 Subjects: – SubjectFull: Meshfree methods Type: general – SubjectFull: Artificial neural networks Type: general – SubjectFull: Partial differential equations Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Strains & stresses (Mechanics) Type: general Titles: – TitleFull: A Mesh-Free Physics-Informed Neural Network Framework for Solving Plane Problems without Locking Issues. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Lin, Zhipeng – PersonEntity: Name: NameFull: Du, Ke – PersonEntity: Name: NameFull: Li, Zepeng IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Summer2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 23834536 Numbering: – Type: volume Value: 12 – Type: issue Value: 3 Titles: – TitleFull: Journal of Applied & Computational Mechanics Type: main |
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