Two-Dimensional Approximation of Thin Piezoelectric Membrane Shells Using Gamma Convergence
In this paper, we consider piezoelectric membrane shells of very small thickness subjected only to mechanical forces and we show that functions which minimize the energy associated with the three-dimensional models converge to the function which minimizes the energy of the two-dimensional model of m...
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| Published in | National Academy of Sciences, India. Proceedings. Section A. Physical Sciences Vol. 90; no. 4; pp. 629 - 635 |
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| Main Author | |
| Format | Journal Article Conference Proceeding |
| Language | English |
| Published |
New Delhi
Springer India
01.10.2020
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
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| Abstract | In this paper, we consider piezoelectric membrane shells of very small thickness subjected only to mechanical forces and we show that functions which minimize the energy associated with the three-dimensional models converge to the function which minimizes the energy of the two-dimensional model of membrane shells. |
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| AbstractList | In this paper, we consider piezoelectric membrane shells of very small thickness subjected only to mechanical forces and we show that functions which minimize the energy associated with the three-dimensional models converge to the function which minimizes the energy of the two-dimensional model of membrane shells. |
| Author | Sabu, N. |
| Author_xml | – sequence: 1 givenname: N. surname: Sabu fullname: Sabu, N. email: sabu@iist.ac.in organization: Department of Mathematics, Indian Institute of Space Science and Technology |
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| Cites_doi | 10.1002/cpa.10048 10.1023/A:1026074730631 10.1007/BF02829610 10.1142/S0252959901000401 10.1016/0045-7825(79)90089-6 10.1007/BF02316975 10.1002/cpa.3160450305 |
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| Copyright | The National Academy of Sciences, India 2019 The National Academy of Sciences, India 2019. |
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| Issue | 4 |
| Keywords | Piezoelectricity Membrane shells Gamma convergence 74K25 |
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| PublicationTitle | National Academy of Sciences, India. Proceedings. Section A. Physical Sciences |
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| References | Ciarlet, Lods, Miara (CR5) 1996; 136 Sabu (CR11) 2000; 68 Ciarlet, Miara (CR6) 1992; 45 CR7 Ciarlet, Destuynder (CR3) 1979; 17 Frieseke, James, Mueller (CR8) 2002; 55 Ciarlet, Lods (CR4) 1996; 136 Sene (CR14) 2001; 25 Ciarlet, Destuynder (CR2) 1979; 18 Sabu (CR13) 2003; 113 Ledret, Raoult (CR10) 1995; 6 Genevey (CR9) 1995; 21 Bourquin, Ciarlet, Geymonat, Raoult (CR1) 1992; 315 Sabu (CR12) 2001; 22B F Bourquin (626_CR1) 1992; 315 PG Ciarlet (626_CR2) 1979; 18 626_CR7 N Sabu (626_CR11) 2000; 68 G Frieseke (626_CR8) 2002; 55 PG Ciarlet (626_CR4) 1996; 136 N Sabu (626_CR12) 2001; 22B PG Ciarlet (626_CR5) 1996; 136 PG Ciarlet (626_CR3) 1979; 17 PG Ciarlet (626_CR6) 1992; 45 A Sene (626_CR14) 2001; 25 K Genevey (626_CR9) 1995; 21 H Ledret (626_CR10) 1995; 6 N Sabu (626_CR13) 2003; 113 |
| References_xml | – volume: 21 start-page: 185 year: 1995 end-page: 197 ident: CR9 article-title: Justification of the two-dimensional shell models by the use of Gamma-convergence theory publication-title: CRM contributor: fullname: Genevey – volume: 55 start-page: 1461 issue: 11 year: 2002 end-page: 1506 ident: CR8 article-title: A theorem on geometric rigidity and derivation of nonlinear plate theory from three dimensional elasticity publication-title: Comm Pure Appl Math doi: 10.1002/cpa.10048 contributor: fullname: Mueller – volume: 68 start-page: 145 year: 2000 end-page: 165 ident: CR11 article-title: Vibrations of piezoelectric flexural shells: two dimensional approximation publication-title: J Elast doi: 10.1023/A:1026074730631 contributor: fullname: Sabu – volume: 113 start-page: 333 issue: 3 year: 2003 end-page: 352 ident: CR13 article-title: Vibrations of piezoelectric shallow shells: two dimensional approximation publication-title: Proc Indian Acad Sci Math Sci doi: 10.1007/BF02829610 contributor: fullname: Sabu – volume: 25 start-page: 1 year: 2001 end-page: 20 ident: CR14 article-title: Modelling of piezoelectric thin plates publication-title: Asymptot Anal contributor: fullname: Sene – volume: 22B start-page: 405 issue: 4 year: 2001 end-page: 416 ident: CR12 article-title: Asymptotic analysis of shallow shells with variable thickness publication-title: Chin Ann Math doi: 10.1142/S0252959901000401 contributor: fullname: Sabu – volume: 18 start-page: 315 year: 1979 end-page: 344 ident: CR2 article-title: A justification of the two dimensional plate model publication-title: J Mec contributor: fullname: Destuynder – volume: 17 start-page: 227 issue: 18 year: 1979 end-page: 258 ident: CR3 article-title: A justification of the nonlinear model of plate theory publication-title: Comp Methods Appl Mech Eng doi: 10.1016/0045-7825(79)90089-6 contributor: fullname: Destuynder – ident: CR7 – volume: 136 start-page: 119 issue: 2 year: 1996 end-page: 161 ident: CR4 article-title: Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equation publication-title: Arch Ration Mech Anal doi: 10.1007/BF02316975 contributor: fullname: Lods – volume: 45 start-page: 327 year: 1992 end-page: 360 ident: CR6 article-title: Justification of the two-dimensional equations of a linearly elastic shell publication-title: Comm Pure Appl Math doi: 10.1002/cpa.3160450305 contributor: fullname: Miara – volume: 136 start-page: 162 year: 1996 end-page: 190 ident: CR5 article-title: Asymptotic analysis of linearly elastic shells. II.Justification of flexural shell equations publication-title: Arch Ration Mech Anal contributor: fullname: Miara – volume: 6 start-page: 549 issue: 9 year: 1995 end-page: 578 ident: CR10 article-title: The nonlinear membrane model as a variational limit of nonlinear three dimensional elasticity publication-title: J Math Pures Appl contributor: fullname: Raoult – volume: 315 start-page: 1017 year: 1992 end-page: 1024 ident: CR1 article-title: Gamma-convergence for the asymptotic theory of plates publication-title: C R Acad Sci Paris Ser I contributor: fullname: Raoult – volume: 18 start-page: 315 year: 1979 ident: 626_CR2 publication-title: J Mec contributor: fullname: PG Ciarlet – volume: 315 start-page: 1017 year: 1992 ident: 626_CR1 publication-title: C R Acad Sci Paris Ser I contributor: fullname: F Bourquin – volume: 136 start-page: 119 issue: 2 year: 1996 ident: 626_CR4 publication-title: Arch Ration Mech Anal doi: 10.1007/BF02316975 contributor: fullname: PG Ciarlet – volume: 22B start-page: 405 issue: 4 year: 2001 ident: 626_CR12 publication-title: Chin Ann Math doi: 10.1142/S0252959901000401 contributor: fullname: N Sabu – volume: 55 start-page: 1461 issue: 11 year: 2002 ident: 626_CR8 publication-title: Comm Pure Appl Math doi: 10.1002/cpa.10048 contributor: fullname: G Frieseke – volume: 6 start-page: 549 issue: 9 year: 1995 ident: 626_CR10 publication-title: J Math Pures Appl contributor: fullname: H Ledret – volume: 136 start-page: 162 year: 1996 ident: 626_CR5 publication-title: Arch Ration Mech Anal contributor: fullname: PG Ciarlet – volume: 17 start-page: 227 issue: 18 year: 1979 ident: 626_CR3 publication-title: Comp Methods Appl Mech Eng doi: 10.1016/0045-7825(79)90089-6 contributor: fullname: PG Ciarlet – ident: 626_CR7 – volume: 25 start-page: 1 year: 2001 ident: 626_CR14 publication-title: Asymptot Anal contributor: fullname: A Sene – volume: 21 start-page: 185 year: 1995 ident: 626_CR9 publication-title: CRM contributor: fullname: K Genevey – volume: 68 start-page: 145 year: 2000 ident: 626_CR11 publication-title: J Elast doi: 10.1023/A:1026074730631 contributor: fullname: N Sabu – volume: 113 start-page: 333 issue: 3 year: 2003 ident: 626_CR13 publication-title: Proc Indian Acad Sci Math Sci doi: 10.1007/BF02829610 contributor: fullname: N Sabu – volume: 45 start-page: 327 year: 1992 ident: 626_CR6 publication-title: Comm Pure Appl Math doi: 10.1002/cpa.3160450305 contributor: fullname: PG Ciarlet |
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| SubjectTerms | Applied and Technical Physics Atomic Convergence Membranes Molecular Optical and Plasma Physics Physics Physics and Astronomy Piezoelectricity Quantum Physics Research Article Three dimensional models Two dimensional models |
| Title | Two-Dimensional Approximation of Thin Piezoelectric Membrane Shells Using Gamma Convergence |
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