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Volumn 88, Issue 1, 2007, Pages 107-122

Plate theory for stressed heterogeneous multilayers of finite bending energy

Author keywords

convergence; Heterostructures; Kirchhoff's plate theory

Indexed keywords


EID: 34347255356     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2007.04.011     Document Type: Article
Times cited : (85)

References (31)
  • 1
    • 0028466769 scopus 로고
    • Dimension reduction in variational problems, asymptotic development in Γ-convergence and thin structures in elasticity
    • Anzellotti G., Baldo S., and Percivale D. Dimension reduction in variational problems, asymptotic development in Γ-convergence and thin structures in elasticity. Asymptot. Anal. 9 (1994) 61-100
    • (1994) Asymptot. Anal. , vol.9 , pp. 61-100
    • Anzellotti, G.1    Baldo, S.2    Percivale, D.3
  • 2
    • 0039030756 scopus 로고    scopus 로고
    • 3D-2D asymptotic analysis for inhomogeneous thin films
    • Braides A., Fonseca I., and Francfort G. 3D-2D asymptotic analysis for inhomogeneous thin films. Indiana Univ. Math. J. 49 (2000) 1367-1404
    • (2000) Indiana Univ. Math. J. , vol.49 , pp. 1367-1404
    • Braides, A.1    Fonseca, I.2    Francfort, G.3
  • 5
    • 0000514542 scopus 로고
    • Methodus Inveniendi Lineas Curvas, Additamentum I: De Curvis Elasticis (1744)
    • Orell Füssli, Bern
    • Euler L. Methodus Inveniendi Lineas Curvas, Additamentum I: De Curvis Elasticis (1744). Opera Omnia Ser. Prima vol. XXIV (1952), Orell Füssli, Bern 231-297
    • (1952) Opera Omnia Ser. Prima , vol.XXIV , pp. 231-297
    • Euler, L.1
  • 6
    • 34347228507 scopus 로고    scopus 로고
    • L.C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations, Conference Board of the AMS, Providence, RI, 1990
  • 7
    • 0013035575 scopus 로고    scopus 로고
    • Rigorous derivation of nonlinear plate theory and geometric rigidity
    • Friesecke G., James R.D., and Müller S. Rigorous derivation of nonlinear plate theory and geometric rigidity. C. R. Acad. Sci. Paris 334 (2002) 173-178
    • (2002) C. R. Acad. Sci. Paris , vol.334 , pp. 173-178
    • Friesecke, G.1    James, R.D.2    Müller, S.3
  • 8
    • 0036384329 scopus 로고    scopus 로고
    • A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
    • Friesecke G., James R.D., and Müller S. A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Comm. Pure Appl. Math. 55 (2002) 1461-1506
    • (2002) Comm. Pure Appl. Math. , vol.55 , pp. 1461-1506
    • Friesecke, G.1    James, R.D.2    Müller, S.3
  • 9
    • 33644602781 scopus 로고    scopus 로고
    • A hierarchy of plate models derived from nonlinear elasticity by Gamma-convergence
    • Friesecke G., James R.D., and Müller S. A hierarchy of plate models derived from nonlinear elasticity by Gamma-convergence. Arch. Rational Mech. Anal. 180 (2006) 183-236
    • (2006) Arch. Rational Mech. Anal. , vol.180 , pp. 183-236
    • Friesecke, G.1    James, R.D.2    Müller, S.3
  • 10
    • 0038783154 scopus 로고    scopus 로고
    • Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence
    • Friesecke G., James R.D., Mora M.G., and Müller S. Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence. C. R. Acad. Sci. Paris 336 (2003) 697-702
    • (2003) C. R. Acad. Sci. Paris , vol.336 , pp. 697-702
    • Friesecke, G.1    James, R.D.2    Mora, M.G.3    Müller, S.4
  • 12
    • 0142026428 scopus 로고    scopus 로고
    • Nanoscroll formation from strained layer heterostructures
    • Grundmann M. Nanoscroll formation from strained layer heterostructures. Appl. Phys. Lett. 83 (2003) 2444-2446
    • (2003) Appl. Phys. Lett. , vol.83 , pp. 2444-2446
    • Grundmann, M.1
  • 13
    • 34347227271 scopus 로고    scopus 로고
    • Preprint Univ. Duisburg-Essen (2007)
    • 2, 2 isometric immersions. Preprint Univ. Duisburg-Essen (2007). http://analysis.math.uni-duisburg.de/publications/preprints/Hornung3.pdf
    • 2, 2 isometric immersions
    • Hornung, P.1
  • 14
    • 34347237457 scopus 로고    scopus 로고
    • T. von Kármán, Festigkeitsprobleme im Maschinenbau, in: Encyclopädie der Mathematischen Wissenschaften, vol. IV/4, Leipzig, 1910, pp. 311-385
  • 15
    • 34347205447 scopus 로고    scopus 로고
    • B. Kirchheim, Geometry and rigidity of microstructures, Habilitation thesis, University of Leipzig, 2001
  • 16
    • 84930244279 scopus 로고
    • Über das Gleichgewicht und die Bewegung einer elastischen Scheibe
    • Kirchhoff G. Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. J. Reine Angew. Math. 40 (1850) 51-88
    • (1850) J. Reine Angew. Math. , vol.40 , pp. 51-88
    • Kirchhoff, G.1
  • 17
    • 0001331060 scopus 로고
    • La modèle membrane non-linéaire comme limite variationnelle de l'élasticité non linéaire tridimensionnelle
    • Le Dret H., and Raoult A. La modèle membrane non-linéaire comme limite variationnelle de l'élasticité non linéaire tridimensionnelle. C. R. Acad. Sci. Paris 317 (1993) 221-226
    • (1993) C. R. Acad. Sci. Paris , vol.317 , pp. 221-226
    • Le Dret, H.1    Raoult, A.2
  • 18
    • 0000312494 scopus 로고
    • The nonlinear membrane model as a variational limit of three-dimensional elasticity
    • Le Dret H., and Raoult A. The nonlinear membrane model as a variational limit of three-dimensional elasticity. J. Math. Pures Appl. 74 (1995) 549-578
    • (1995) J. Math. Pures Appl. , vol.74 , pp. 549-578
    • Le Dret, H.1    Raoult, A.2
  • 19
    • 1842611371 scopus 로고    scopus 로고
    • The membrane shell model in nonlinear elasticity: a variational asymptotic derivation
    • Le Dret H., and Raoult A. The membrane shell model in nonlinear elasticity: a variational asymptotic derivation. J. Nonlinear Sci. 6 (1996) 59-84
    • (1996) J. Nonlinear Sci. , vol.6 , pp. 59-84
    • Le Dret, H.1    Raoult, A.2
  • 22
    • 0000148308 scopus 로고
    • On spherical image maps whose Jacobians do not change signs
    • Hartman P., and Nirenberg L. On spherical image maps whose Jacobians do not change signs. Amer. J. Math. 81 (1959) 901-920
    • (1959) Amer. J. Math. , vol.81 , pp. 901-920
    • Hartman, P.1    Nirenberg, L.2
  • 23
    • 4644250661 scopus 로고    scopus 로고
    • On the Sobolev space of isometric immersions
    • Pakzad M.R. On the Sobolev space of isometric immersions. J. Differential Geom. 66 (2004) 47-69
    • (2004) J. Differential Geom. , vol.66 , pp. 47-69
    • Pakzad, M.R.1
  • 24
    • 0012990486 scopus 로고    scopus 로고
    • Un justification partielle du modèle de plaque en flexion par Γ-convergence
    • Pantz O. Un justification partielle du modèle de plaque en flexion par Γ-convergence. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 587-592
    • (2001) C. R. Acad. Sci. Paris Sér. I Math. , vol.332 , pp. 587-592
    • Pantz, O.1
  • 25
    • 0001347396 scopus 로고
    • Extensions of the theorem of Gauss on the spherical representation to the case of surfaces of bounded extrinsic curvature
    • Pogorelov A.V. Extensions of the theorem of Gauss on the spherical representation to the case of surfaces of bounded extrinsic curvature. Dokl. Akad. Nauk SSSR (N.S.) 111 (1956) 945-947
    • (1956) Dokl. Akad. Nauk SSSR (N.S.) , vol.111 , pp. 945-947
    • Pogorelov, A.V.1
  • 27
    • 34548101929 scopus 로고    scopus 로고
    • B. Schmidt, Minimal energy configurations of strained multi-layers, Calc. Var. Partial Differential Equations (2007), doi:10.1007/s00526-007-0099-4
  • 28
    • 34347207424 scopus 로고    scopus 로고
    • B. Schmidt, Effective theories for thin elastic films, PhD thesis, University of Leipzig, 2006
  • 29
    • 0035826219 scopus 로고    scopus 로고
    • Thin solid films roll up into nanotubes
    • Schmidt O.G., and Eberl K. Thin solid films roll up into nanotubes. Nature 410 (2001) 168
    • (2001) Nature , vol.410 , pp. 168
    • Schmidt, O.G.1    Eberl, K.2
  • 30
    • 0034422268 scopus 로고    scopus 로고
    • Heterogeneous thin films of martensitic materials
    • Shu Y.C. Heterogeneous thin films of martensitic materials. Arch. Ration. Mech. Anal. 153 (2000) 39-90
    • (2000) Arch. Ration. Mech. Anal. , vol.153 , pp. 39-90
    • Shu, Y.C.1
  • 31
    • 0031199186 scopus 로고    scopus 로고
    • An analytical model for predicting residual stress in progressively deposited coatings I
    • Tsui J.C., and Clyne T.W. An analytical model for predicting residual stress in progressively deposited coatings I. Thin Solid Films 306 (1997) 23-33
    • (1997) Thin Solid Films , vol.306 , pp. 23-33
    • Tsui, J.C.1    Clyne, T.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.