View in EDS

Study of solutions of the elasticity theory equations in a spherical coordinate system.

Saved in:
Bibliographic Details
Title: Study of solutions of the elasticity theory equations in a spherical coordinate system.
Authors: Revenko, V. P.1 (AUTHOR) victor.rev.12@gmail.com
Source: Materials Science. Nov2025, Vol. 61 Issue 3, p366-374. 9p.
Subjects: Elasticity, Spherical coordinates, Stress concentration, Strains & stresses (Mechanics), Elastic solids
Abstract: The linear model of elastic theory for an isotropic body is considered. The Navier equation solution is used in the curvilinear orthogonal coordinate system. It is proven that the complete three-dimensional solution of the system of equations of elasticity theory in the spherical coordinate system is expressed through three harmonic displacement functions. Analytical formulas for expressing displacements and stresses, which are written relative to the elevation angle ϑ are given for the first time. It is shown that when the displacement functions do not depend on the azimuth angular coordinate φ, the stress-strain state is divided into a spherical axisymmetric stress, which is described by two functions, and the stress state of pure twisting, which is described by one function. It is established that if elastic displacements and stresses depend on the radial variable only, they describe one stress state in the sphere, which corresponds to the effect of uniform pressure on its surface. The basic solutions, which correspond to the main force vector components, are built for an elastic sphere. [ABSTRACT FROM AUTHOR]
Copyright of Materials Science 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
Header DbId: egs
DbLabel: Engineering Source
An: 190358852
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Study of solutions of the elasticity theory equations in a spherical coordinate system.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Revenko%2C+V%2E+P%2E%22">Revenko, V. P.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> victor.rev.12@gmail.com</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Materials+Science%22">Materials Science</searchLink>. Nov2025, Vol. 61 Issue 3, p366-374. 9p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Elasticity%22">Elasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Spherical+coordinates%22">Spherical coordinates</searchLink><br /><searchLink fieldCode="DE" term="%22Stress+concentration%22">Stress concentration</searchLink><br /><searchLink fieldCode="DE" term="%22Strains+%26+stresses+%28Mechanics%29%22">Strains & stresses (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Elastic+solids%22">Elastic solids</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The linear model of elastic theory for an isotropic body is considered. The Navier equation solution is used in the curvilinear orthogonal coordinate system. It is proven that the complete three-dimensional solution of the system of equations of elasticity theory in the spherical coordinate system is expressed through three harmonic displacement functions. Analytical formulas for expressing displacements and stresses, which are written relative to the elevation angle ϑ are given for the first time. It is shown that when the displacement functions do not depend on the azimuth angular coordinate φ, the stress-strain state is divided into a spherical axisymmetric stress, which is described by two functions, and the stress state of pure twisting, which is described by one function. It is established that if elastic displacements and stresses depend on the radial variable only, they describe one stress state in the sphere, which corresponds to the effect of uniform pressure on its surface. The basic solutions, which correspond to the main force vector components, are built for an elastic sphere. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Materials Science 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.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=190358852
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s11003-025-01002-w
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 9
        StartPage: 366
    Subjects:
      – SubjectFull: Elasticity
        Type: general
      – SubjectFull: Spherical coordinates
        Type: general
      – SubjectFull: Stress concentration
        Type: general
      – SubjectFull: Strains & stresses (Mechanics)
        Type: general
      – SubjectFull: Elastic solids
        Type: general
    Titles:
      – TitleFull: Study of solutions of the elasticity theory equations in a spherical coordinate system.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Revenko, V. P.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 11
              Text: Nov2025
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 1068820X
          Numbering:
            – Type: volume
              Value: 61
            – Type: issue
              Value: 3
          Titles:
            – TitleFull: Materials Science
              Type: main
ResultId 1