Mathematical model for lateral deflection of a circular plate under the cosine load – spherical rigid body application.
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| Title: | Mathematical model for lateral deflection of a circular plate under the cosine load – spherical rigid body application. |
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| Authors: | Kotšmíd, Stanislav1 (AUTHOR) stanislav.kotsmid@tuzvo.sk |
| Source: | Engineering Computations. 2026, Vol. 43 Issue 5, p1830-1844. 15p. |
| Subjects: | Deflection (Mechanics), Structural plates, Mathematical models, Elasticity, Mechanical loads, Finite element method, Spheres |
| Abstract: | Purpose: The purpose of this paper is to present a mathematical model to calculate the lateral deflection of a circular isotropic plate with constant thickness under the cosine load within the plate theory limitations. Design/methodology/approach: The mathematical model is derived on the basis of the governing nonhomogeneous differential equation for the plate theory, where the function of lateral deflection is shown in the form of a cosine integral and power series form, respectively. The accuracy of the mathematical model is verified by numerical analyses performed by the finite element method. Findings: A good agreement between the presented model and numerical analyses is obtained in terms of the elastic theory and the assumption of small deformation, as well as when using the model for a spherical rigid body loading within the studied conditions, where all discrepancies are below 4.2%. The presented mathematical model may be applied to calculate the lateral deflection of a plate loaded by a spherical rigid body where the cosine load is assumed on the basis of the bearing hypothesis. Research limitations/implications: The research limitations fall into the constant thickness, homogenous and isotropic material, small deformation theory and axisymmetric behavior of the studied parts. Originality/value: Except the pure cosine load, applied on the entire plate surface, a partially placed load is investigated as well, which has a practical relevance when loading the plate by a spherical rigid body. The presented mathematical model provides a convenient calculation when numerical analysis is not available, while the paper shows a load diversity under different magnitudes as well. [ABSTRACT FROM AUTHOR] |
| Copyright of Engineering Computations is the property of Emerald Publishing Limited 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: 194143654 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Mathematical model for lateral deflection of a circular plate under the cosine load – spherical rigid body application. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kotšmíd%2C+Stanislav%22">Kotšmíd, Stanislav</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> stanislav.kotsmid@tuzvo.sk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Engineering+Computations%22">Engineering Computations</searchLink>. 2026, Vol. 43 Issue 5, p1830-1844. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Deflection+%28Mechanics%29%22">Deflection (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+plates%22">Structural plates</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Elasticity%22">Elasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+loads%22">Mechanical loads</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Spheres%22">Spheres</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Purpose: The purpose of this paper is to present a mathematical model to calculate the lateral deflection of a circular isotropic plate with constant thickness under the cosine load within the plate theory limitations. Design/methodology/approach: The mathematical model is derived on the basis of the governing nonhomogeneous differential equation for the plate theory, where the function of lateral deflection is shown in the form of a cosine integral and power series form, respectively. The accuracy of the mathematical model is verified by numerical analyses performed by the finite element method. Findings: A good agreement between the presented model and numerical analyses is obtained in terms of the elastic theory and the assumption of small deformation, as well as when using the model for a spherical rigid body loading within the studied conditions, where all discrepancies are below 4.2%. The presented mathematical model may be applied to calculate the lateral deflection of a plate loaded by a spherical rigid body where the cosine load is assumed on the basis of the bearing hypothesis. Research limitations/implications: The research limitations fall into the constant thickness, homogenous and isotropic material, small deformation theory and axisymmetric behavior of the studied parts. Originality/value: Except the pure cosine load, applied on the entire plate surface, a partially placed load is investigated as well, which has a practical relevance when loading the plate by a spherical rigid body. The presented mathematical model provides a convenient calculation when numerical analysis is not available, while the paper shows a load diversity under different magnitudes as well. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Engineering Computations is the property of Emerald Publishing Limited 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 1830 Subjects: – SubjectFull: Deflection (Mechanics) Type: general – SubjectFull: Structural plates Type: general – SubjectFull: Mathematical models Type: general – SubjectFull: Elasticity Type: general – SubjectFull: Mechanical loads Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Spheres Type: general Titles: – TitleFull: Mathematical model for lateral deflection of a circular plate under the cosine load – spherical rigid body application. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kotšmíd, Stanislav IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02644401 Numbering: – Type: volume Value: 43 – Type: issue Value: 5 Titles: – TitleFull: Engineering Computations Type: main |
| ResultId | 1 |
