Dynamic modeling and determination of effective properties of smart composite plates with rapidly varying thickness

International Journal of Engineering Science

Volumn 56, Issue , 2012, Pages 63-85

  Hadjiloizi, D A ^a   Georgiades, A V ^a   Kalamkarov, A L ^b  

^a CYPRUS UNIVERSITY OF TECHNOLOGY   (Cyprus)

^b DALHOUSIE UNIVERSITY   (Canada)

Author keywords

Asymptotic homogenization; Effective properties; Piezo magneto thermo elastic thin smart composite plate

Indexed keywords

ANISOTROPIC PLATES; ASYMPTOTIC HOMOGENIZATION; COMPOSITE PLATES; DEVELOPED MODEL; DYNAMIC EQUILIBRIA; DYNAMIC MODELING; DYNAMIC PROBLEM; EFFECTIVE PROPERTY; ELECTRIC DISPLACEMENT; ELECTRICAL CONDUCTIVITY; GENERAL EXPRESSION; GOVERNING EQUATIONS; MAXWELL'S EQUATIONS; MECHANICAL DISPLACEMENTS; MICROMECHANICAL MODEL; MIDDLE LAYER; MULTISCALES; PIEZOMAGNETIC; PRODUCT PROPERTY; SMART COMPOSITE PLATE; SMART COMPOSITES; THERMAL BALANCE; THIN PLATE; THREE DIMENSIONAL FORMULATION; TIME VARYING; UNIT CELLS; VARYING THICKNESS;

ELECTRIC CONDUCTIVITY; ELECTRIC FIELDS; HEAT FLUX; MAGNETIC FIELDS; MAGNETOS; MAXWELL EQUATIONS; PLATES (STRUCTURAL COMPONENTS); STRESSES; THERMOELASTICITY;

MECHANICAL PROPERTIES;

EID: 84861116423     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2012.02.007     Document Type: Article

References (65)

1. I.V. Andrianov, V.V. Danishevs'kyy, and A.L. Kalamkarov Asymptotic justification of the three-phase composite model Composite Structures 77 3 2007 395 404 (Pubitemid 44767161)
2. I.V. Andrianov, V.A. Lesnichaya, and L.I. Manevich Homogenization methods in the statics and dynamics of ribbed shells 1985 Nauka Moscow
3. I.V. Andrianov, and L.I. Manevich Shell design using the homogenization method Uspekhi Mekhaniki 6 1983 3 29
4. M. Avellaneda, and G. Harshé Magnetoelectric effect in piezoelectric/magnetostrictive multilayer (2-2) composites Journal of Intelligent Material Systems and Structures 5 1994 501 513
5. N. Bakhvalov, and G. Panasenko Homogenisation: Averaging processes in periodic media 1984 Kluwer Academic Publishers Netherlands
6. A. Bensoussan, J.L. Lions, and G. Papanicolaou Asymptotic analysis for periodic structures 1978 North-Holland Publisher Amsterdam
7. M.I. Bichurin, V.N. Petrov, S.V. Averkin, and E. Liverts Present status of theoretical modeling the magnetoelectric effect in magnetostrictive- piezoelectric nanostructures. Part I: Low frequency electromechanical resonance ranges Journal of Applied Physics 107 5 2010 053904(1) 053904(11)
8. M.I. Bichurin, V.N. Petrov, and G. Srinivasan Modeling of magnetoelectric effect in ferromagnetic/piezoelectric multilayer composites Ferroelectrics 280 2002 165 175 (Pubitemid 44104350)
9. J. Bravo-Castillero, R. Rodrigues-Ramos, H. Mechkour, J. Otero, and F.J. Sabina Homogenization of magneto-electro-elastic multilaminated materials Quarterly Journal of Mechanics and Applied Mathematics 61 3 2008 311 332
10. B. Budiansky On the elastic moduli of some heterogeneous materials Journal of the Mechanics and Physics of Solids 13 1965 223 227
11. D. Caillerie Equations de la diffusion stationnaire dans un domaine comportant une distribution périodique d'inclusions aplaties de grande conductivité Comptes Rendus de l' Academie des Sciences - Serie I 292 1 1981 115 118
12. D. Caillerie Homogénéisation des équations de la diffusion dans les domaines cylindriques aplatis RAIRO Analyse Numérique 15 1981 295 319
13. K. Challagulla, A.V. Georgiades, and A.L. Kalamkarov Asymptotic homogenization modeling of thin network structures Composite Structures 79 3 2007 432 444 (Pubitemid 46351861)
14. K.S. Challagulla, A.V. Georgiades, and A.L. Kalamkarov Asymptotic homogenization modeling of smart composite generally orthotropic grid-reinforced shells. Part I: Theory European Journal of Mechanics A: Solids 29 2010 530 540
15. R.M. Christensen A critical evaluation for a class of micromechanics models Journal of the Mechanics and Physics of Solids 38 1990 379 404
16. D. Cioranescu, and P. Donato An Introduction to homogenization 1999 Oxford University Press Oxford
17. A. Daga, N. Ganesan, and K. Shankar Studies on magnetoelectric effect for magneto-electro-elastic cylinder using finite element method Multidiscipline Modeling in Materials and Structures 5 3 2009 307 310
18. F. Devries, H. Dumontet, G. Duvaut, and F. Lene Homogenization and damage for composite structures International Journal for Numerical Methods in Engineering 27 1989 285 298 (Pubitemid 20645029)
19. Duvaut, G. (1976). Analyse fonctionnelle et méchanique des milieux continus. In Proceeding of the 14th IUTAM congress (Vol.1, pp. 119-132), 30 August-4 September, Delft.
20. Duvaut, G. (1977). Comportement macroscopique d'une plaque perforée périodiquement. Lecture notes in mathematics (Vol. 594, pp. 131-145).
21. G. Duvaut, and A-M Metellus Homogénéisation d'une plaque mince en flexion de structure périodique et symétrique Comptes Rendus des seances de l' Academie des Sciences - Serie A 283 1976 947 950
22. A.V. Georgiades, K.S. Challagulla, and A.L. Kalamkarov Modeling of the thermopiezoelastic behavior of prismatic smart composite structures made of orthotropic materials Composites Part B: Engineering 37 7-8 2006 569 582 (Pubitemid 44128909)
23. A.V. Georgiades, K.S. Challagulla, and A.L. Kalamkarov Asymptotic homogenization modeling of smart composite generally orthotropic grid-reinforced shells. Part II: Applications European Journal of Mechanics A. Solids 29 2010 541 556
24. J.M. Guedes, and N. Kikuchi Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods Computer Methods in Applied Mechanics and Engineering 83 1990 143 198
25. J.C. Halpin, and N.J. Pagano The laminate approximation for randomly oriented fibrous composites Journal of Composite Materials 3 1966 720 724
26. Z. Hashin The elastic moduli of heterogeneous materials Journal of Applied Mechanics 29 1962 143 150
27. Z. Hashin, and S. Shtrikman A variational approach to the theory of elastic behavior of multiphase materials Journal of the Mechanics and Physics of Solids 11 1963 127 140
28. Z. Hashin, and S. Shtrikman Conductivity of polycrystals Physical Review 130 1 1963 129 133
29. E.M. Hassan, A.L. Kalamkarov, A.V. Georgiades, and K.S. Challagulla Asymptotic homogenization model for smart 3D grid-reinforced composite structures with generally orthotropic constituents Smart Materials & Structures 18 7 2009 Article ID: 075006
30. A.V. Hershey The elasticity of an isotropic aggregate of anisotropic cubic crystals Journal of Applied Mechanics 21 1954 236 240
31. R. Hill A self-consistent mechanics of composite materials Journal of the Mechanics and Physics of Solids 13 1965 213 222
32. A.L. Kalamkarov Composite and reinforced elements of construction 1992 Wiley New York
33. A.L. Kalamkarov, and A.V. Georgiades Modeling of smart composites on account of actuation, thermal conductivity and hygroscopic absorption Composites, Part B: Engineering 33 2002 141 152 (Pubitemid 34156698)
34. A.L. Kalamkarov, and A.V. Georgiades Micromechanical modeling of smart composite structures Smart Materials & Structures 11 2002 423 434 (Pubitemid 34758952)
35. A.L. Kalamkarov, and A.G. Kolpakov Analysis, design and optimization of composite structures 1997 Wiley New York
36. A.L. Kalamkarov, and A.G. Kolpakov A new asymptotic model for a composite piezoelastic plate International Journal of Solids and Structures 38 2001 6027 6044 (Pubitemid 32646701)
37. R.V. Kohn, and M. Vogelius A new model for thin plates with rapidly varying thickness International Journal of Solids and Structures 20 1984 333 350 (Pubitemid 14546314)
38. R.V. Kohn, and M. Vogelius A new model for thin plates with rapidly varying thickness, II: A convergence proof Quarterly of Applied Mathematics 43 1985 1 22 (Pubitemid 15599356)
39. R.V. Kohn, and M. Vogelius A new model for thin plates with rapidly varying thickness, III: Comparison of different scalings Quarterly of Applied Mathematics 44 1986 35 48 (Pubitemid 17493277)
40. G.W. Milton Bounds on the complex permittivity of a two component composite material Journal of Applied Physics 52 8 1981 5286 5293 (Pubitemid 12431153)
41. G.W. Milton Bounds on the elastic and transport properties of two-component composites Journal of the Mechanics and Physics of Solids 30 3 1982 177 191 (Pubitemid 12550192)
42. G.W. Milton, and R.V. Kohn Variational bounds on the effective moduli of anisotropic composites Journal of the Mechanics and Physics of Solids 36 1988 597 629
43. T. Mori, and K. Tanaka Average stress in matrix and average energy of materials with misfitting inclusions Acta Metallurgica et Materialia 21 1973 571 574
44. C.-W. Nan, M.I. Bichurin, S. Dong, D. Viehland, and G. Srinivasan Multiferroic magnetoelectric composites: Historical perspective, status, and future directions Journal of Applied Physics 031101 2008 1 35
45. S. Nemat-Nasser, and M. Hori Micromechanics overall properties of heterogeneous solids 1993 Elsevier Amsterdam
46. R.E. Newnham, D.P. Skinner, and L.E. Cross Connectivity and piezoelectric-pyroelectric composites Materials Research Bulletin 13 1978 525 536
47. Y. Ni, and A.G. Khachaturyan Phase field approach for strain-induced magnetoelectric effect in multiferroic composites Journal of Applied Physics 102 2007 113506(1) 113506(10)
48. Y. Ni, S. Priya, and A.G. Khachaturyan Modeling of magnetoelectric effect in polycrystalline multiferroic laminates influenced by the orientations of applied electric/magnetic fields Journal of Applied Physics 105 2009 083914(1) 083914(4)
49. G.M. Odegard, T.S. Gates, K.E. Wise, C. Park, and E.J. Siochi Constitutive modeling of nanotube-reinforced polymer composites Composites Science and Technology 63 11 2003 1671 1687 (Pubitemid 36914805)
50. I.A. Osaretin, and R.G. Rojas Theoretical model for the magnetoelectric effect in magnetostrictive/piezoelectric composites Physical Review B 82 2010 174415(1) 174415(8)
51. D.A. Pan, S.G. Zhang, A.A. Volinsky, and L.J. Qiao Simple model of the magnetoelectric effect in layered cylindrical composites Journal of Physics D. Applied Physics 41 2008 205008(1) 205008(5)
52. G.C. Saha, A.L. Kalamkarov, and A.V. Georgiades Micromechanical analysis of effective piezoelastic properties of smart composite sandwich shells made of generally orthotropic materials Smart Materials & Structures 16 3 2007 866 883 (Pubitemid 46804859)
53. E. Sanchez-Palencia Non-homogeneous media and vibration theory Lecture notes in physics 1980 Springer-Verlag Berlin
54. G.P. Sendeckyj Elastic behavior of composites Composite materials Mechanics of composite materials Vol. 2 1974 Academic Press New York
55. I. Sevostianov, and M. Kachanov Effect of interphase layers on the overall elastic and conductive properties of matrix composites: Applications to nanosize inclusion International Journal of Solids and Structures 44 2007 1304 1315 (Pubitemid 44749986)
56. G. Srinivasan, E.T. Rasmussen, J. Gallegos, R. Srinivasan, Yu.-I. Bokhan, and V.M. Laletin Magnetoelectric bilayer and multilayer structures of magnetostrictive and piezoelectric oxides Physical Review B. 64 2001 214408(1) 214408(6) (Pubitemid 33140870)
57. S. Torquato, and G. Stell Microstructure of two-phase random media Journal of Chemical Physics 82 2 1985 980 987
58. Tsai, S. W. (1992). Theory of composites design. Dayton, OH.
59. C.H. Tsang, K.H. Chau, C.K. Wong, and F.G. Shin Modeling of the magnetoelectric effect of three-phase multiferroic particulate composites Ferroelectrics 100 2008 177 197
60. V.V. Vasiliev Mechanics of composite structures 1993 Taylor and Francis Washington, DC
61. V.V. Vasiliev, and Yu.M. Tarnopol'skii Composite materials 1990 Mashinostroenie Moscow [in Russian]
62. J.R. Vinson The behavior of shells composed of isotropic and composite materials 1993 Kluwer Dordrecht
63. J.R. Vinson, and R.L. Sierokowski The behavior of structures composed of composite materials 1986 Nijhoff Dordrecht
64. L.J. Walpole On the bounds for the overall elastic moduli of inhomogeneous systems - I Journal of the Mechanics and Physics of Solids 14 1966 151 162
65. G.J. Weng, M. Taya, and H. Abé Micromechanics and inhomogeneity The T. Mura 65th anniversary volume 1990 Springer New York