Seven-parameter quadrilateral scaled boundary spectral shell elements with a general stress recovery procedure.
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| Title: | Seven-parameter quadrilateral scaled boundary spectral shell elements with a general stress recovery procedure. |
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| Authors: | Li, Jianghuai1 (AUTHOR) lijianghuai@nbu.edu.cn |
| Source: | Computational Mechanics. Jun2026, Vol. 77 Issue 6, p1983-2012. 30p. |
| Subjects: | Spectral element method, Structural shells, Differential quadrature method, Finite element method, Mechanical stress analysis, Quadrilaterals |
| Abstract: | This paper presents new shell elements that require only the shell midsurface to be discretized, utilize complete three-dimensional constitutive laws, and contain only seven translational degrees of freedom along each nodal normal. The middle surface of such a shell element is approximated by a variable-order quadrilateral spectral element, which is scaled along the thickness to represent the full shell geometry. Along the nodal normal, the in-plane displacement fields are assumed to be linear by interpolating the displacements at the top and bottom points, while the transverse displacement field is quadratic by interpolating the displacements at the top, middle, and bottom points. Lagrange polynomials are employed for the interpolation and the coefficients of the linear and quadratic terms are respectively scaled by the shell thickness and its square to reduce the condition number of the global stiffness matrix particularly for thin shells. The inverse Jacobian matrix is approximated as a quadratic matrix polynomial using Neumann expansion to guarantee the solution accuracy for thick curved shells. The assumed natural strain method is applied to alleviate transverse shear locking, membrane locking, and curvature thickness locking. A general procedure for recovering the transverse stresses is proposed by analytically integrating the static equilibrium equations along the thickness direction, and the involved functional derivatives with respect to the in-plane coordinates are evaluated via the differential quadrature method. The capabilities of the developed shell elements are sufficiently demonstrated through numerical examples. [ABSTRACT FROM AUTHOR] |
| Copyright of Computational 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194724358 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Seven-parameter quadrilateral scaled boundary spectral shell elements with a general stress recovery procedure. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Li%2C+Jianghuai%22">Li, Jianghuai</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lijianghuai@nbu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computational+Mechanics%22">Computational Mechanics</searchLink>. Jun2026, Vol. 77 Issue 6, p1983-2012. 30p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Spectral+element+method%22">Spectral element method</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+shells%22">Structural shells</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+quadrature+method%22">Differential quadrature method</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+stress+analysis%22">Mechanical stress analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Quadrilaterals%22">Quadrilaterals</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper presents new shell elements that require only the shell midsurface to be discretized, utilize complete three-dimensional constitutive laws, and contain only seven translational degrees of freedom along each nodal normal. The middle surface of such a shell element is approximated by a variable-order quadrilateral spectral element, which is scaled along the thickness to represent the full shell geometry. Along the nodal normal, the in-plane displacement fields are assumed to be linear by interpolating the displacements at the top and bottom points, while the transverse displacement field is quadratic by interpolating the displacements at the top, middle, and bottom points. Lagrange polynomials are employed for the interpolation and the coefficients of the linear and quadratic terms are respectively scaled by the shell thickness and its square to reduce the condition number of the global stiffness matrix particularly for thin shells. The inverse Jacobian matrix is approximated as a quadratic matrix polynomial using Neumann expansion to guarantee the solution accuracy for thick curved shells. The assumed natural strain method is applied to alleviate transverse shear locking, membrane locking, and curvature thickness locking. A general procedure for recovering the transverse stresses is proposed by analytically integrating the static equilibrium equations along the thickness direction, and the involved functional derivatives with respect to the in-plane coordinates are evaluated via the differential quadrature method. The capabilities of the developed shell elements are sufficiently demonstrated through numerical examples. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Computational 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/s00466-025-02738-7 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 30 StartPage: 1983 Subjects: – SubjectFull: Spectral element method Type: general – SubjectFull: Structural shells Type: general – SubjectFull: Differential quadrature method Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Mechanical stress analysis Type: general – SubjectFull: Quadrilaterals Type: general Titles: – TitleFull: Seven-parameter quadrilateral scaled boundary spectral shell elements with a general stress recovery procedure. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Li, Jianghuai IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 01787675 Numbering: – Type: volume Value: 77 – Type: issue Value: 6 Titles: – TitleFull: Computational Mechanics Type: main |
| ResultId | 1 |
