SMALL DEFORMATIONS SUPERIMPOSED UPON THE SYMMETRICAL EXPANSION OF A SPHERICAL SHELL.
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| Title: | SMALL DEFORMATIONS SUPERIMPOSED UPON THE SYMMETRICAL EXPANSION OF A SPHERICAL SHELL. |
|---|---|
| Authors: | HILL, JAMES M.1, ARRIGO, DANIEL J.1 |
| Source: | Quarterly Journal of Mechanics & Applied Mathematics. 1996, Vol. 49 Issue 3, p337-351. 15p. |
| Subjects: | Superimposed coding, Spherical shells (Engineering), Strains & stresses (Mechanics), Symmetry (Physics), Mechanical buckling, Reciprocals (Mathematics) |
| Abstract: | The problem of small deformations of isotropic incompressible hyperelastic materials superimposed upon the symmetrical expansion of a spherical shell is re-examined making use of a recent new solution applying to the material with a ‘modified’ Varga strain-energy function. This particular strain-energy function has not been previously used in the literature and comprises the Varga strain-energy function with an additional term involving the reciprocals of the principal stretches. This new term enhances the physical applicability of the Varga strain-energy function and this aspect is briefly examined in the Appendix. Use of the new solution in the present context appears to conflict with previous work of the first author. This apparent conflict is fully resolved and it is shown that previously-used expansions for the pressure function and the response coefficients are only valid for restricted forms of the strain-energy function. Generally, an additional term arises in the expansion of these quantities, which appears not to have been identified by previous authors. This particular problem illustrates the need to exercise caution in formulating the correct structure of the expansions, which almost certainly is a relevant issue for many other small on large problems. The solutions obtained are utilized for the problem of the determination of the critical pressures for the buckling of thick-walled spherical shells under uniform external pressure and some illustrative numerical results are presented for a particular buckling mode. [ABSTRACT FROM AUTHOR] |
| Copyright of Quarterly Journal of Mechanics & Applied Mathematics is the property of Oxford University Press / USA 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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| Items | – Name: Title Label: Title Group: Ti Data: SMALL DEFORMATIONS SUPERIMPOSED UPON THE SYMMETRICAL EXPANSION OF A SPHERICAL SHELL. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22HILL%2C+JAMES+M%2E%22">HILL, JAMES M.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22ARRIGO%2C+DANIEL+J%2E%22">ARRIGO, DANIEL J.</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Quarterly+Journal+of+Mechanics+%26+Applied+Mathematics%22">Quarterly Journal of Mechanics & Applied Mathematics</searchLink>. 1996, Vol. 49 Issue 3, p337-351. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Superimposed+coding%22">Superimposed coding</searchLink><br /><searchLink fieldCode="DE" term="%22Spherical+shells+%28Engineering%29%22">Spherical shells (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Strains+%26+stresses+%28Mechanics%29%22">Strains & stresses (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetry+%28Physics%29%22">Symmetry (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+buckling%22">Mechanical buckling</searchLink><br /><searchLink fieldCode="DE" term="%22Reciprocals+%28Mathematics%29%22">Reciprocals (Mathematics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The problem of small deformations of isotropic incompressible hyperelastic materials superimposed upon the symmetrical expansion of a spherical shell is re-examined making use of a recent new solution applying to the material with a ‘modified’ Varga strain-energy function. This particular strain-energy function has not been previously used in the literature and comprises the Varga strain-energy function with an additional term involving the reciprocals of the principal stretches. This new term enhances the physical applicability of the Varga strain-energy function and this aspect is briefly examined in the Appendix. Use of the new solution in the present context appears to conflict with previous work of the first author. This apparent conflict is fully resolved and it is shown that previously-used expansions for the pressure function and the response coefficients are only valid for restricted forms of the strain-energy function. Generally, an additional term arises in the expansion of these quantities, which appears not to have been identified by previous authors. This particular problem illustrates the need to exercise caution in formulating the correct structure of the expansions, which almost certainly is a relevant issue for many other small on large problems. The solutions obtained are utilized for the problem of the determination of the critical pressures for the buckling of thick-walled spherical shells under uniform external pressure and some illustrative numerical results are presented for a particular buckling mode. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Quarterly Journal of Mechanics & Applied Mathematics is the property of Oxford University Press / USA 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: 10.1093/qjmam/49.3.337 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 337 Subjects: – SubjectFull: Superimposed coding Type: general – SubjectFull: Spherical shells (Engineering) Type: general – SubjectFull: Strains & stresses (Mechanics) Type: general – SubjectFull: Symmetry (Physics) Type: general – SubjectFull: Mechanical buckling Type: general – SubjectFull: Reciprocals (Mathematics) Type: general Titles: – TitleFull: SMALL DEFORMATIONS SUPERIMPOSED UPON THE SYMMETRICAL EXPANSION OF A SPHERICAL SHELL. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: HILL, JAMES M. – PersonEntity: Name: NameFull: ARRIGO, DANIEL J. IsPartOfRelationships: – BibEntity: Dates: – D: 03 M: 01 Text: 1996 Type: published Y: 1996 Identifiers: – Type: issn-print Value: 00335614 Numbering: – Type: volume Value: 49 – Type: issue Value: 3 Titles: – TitleFull: Quarterly Journal of Mechanics & Applied Mathematics Type: main |
| ResultId | 1 |
