Electro-mechanical analysis of composite and sandwich multilayered structures by shell elements with node-dependent kinematics

References

• R.D. Mindlin, Forced thickness-shear and flexural vibrations of piezoelectric crystal plates, J. Appl. Phys 23 (1952), pp. 83–91. doi:10.1063/1.1701983
   Web of Science ®Google Scholar
• E.P. EerNisse, Variational method for electroelastic vibration analysis, IEEE Trans. Sonics Ultrasonics 14 (4) (1967), pp. 153–213. doi:10.1109/T-SU.1967.29431
   Google Scholar
• H.F. Tiersten and R.D. Mindlin, Forced vibrations of piezoelectric crystal plates, Q. Appl. Math. 20 (2) (1962), pp. 107–126. doi:10.1090/qam/99964
   Google Scholar
• H.F. Tiersten, Linear piezoelectric plate vibrations, New York Plenum Press, New York, 1969.
   Google Scholar
• D.A. Saravanos and P.R. Heyliger, Mechanics and computational models for laminated piezoelectric beams, plates and shells, Appl. Mechanics Rev. 52 (10) (1999), pp. 305–324. doi:10.1115/1.3098918
   Google Scholar
• S. Kapuria, A coupled zig-zag third-order theory for piezoelectric hybrid cross-ply plates, J. Appl. Mechanics 71 (2004), pp. 604–618. doi:10.1115/1.1767170
   Web of Science ®Google Scholar
• C. Ossadzow-David and M. Touratier, A multilayered piezoelectric shell theory, Compos. Sci. Technol 64 (2004), pp. 2121–2158. doi:10.1016/j.compscitech.2004.03.005
   Web of Science ®Google Scholar
• P. Heyliger, K.C. Pei, and D.A. Saravanos, Layerwise mechanics and finite element model for laminated piezoelectric shells, AIAA J. 34 (11) (1996), pp. 2353–2413. doi:10.2514/3.13401
   Google Scholar
• D. Ballhause, M. D’Ottavio, B. Kroplin, and E. Carrera, A unified formulation to assess multilayered theories for piezoelectric plates, Comput. Struct 83 (15–16) (2005), pp. 1217–1235. doi:10.1016/j.compstruc.2004.09.015
   Web of Science ®Google Scholar
• M. D’Ottavio, D. Ballhause, B. Kroplin, and E. Carrera, Closed-form solutions for the free-vibration problem of multilayered piezoelectric shells, Comput. Struct 84 (2006), pp. 1506–1524. doi:10.1016/j.compstruc.2006.01.030
   Web of Science ®Google Scholar
• A. Benjeddou, J. Deu, and S. Letombe, Free vibrations of simply-supported piezoelectric adaptive plates: An exact sandwich formulation, Thin-Walled Struct 40 (2002), pp. 573–666. doi:10.1016/S0263-8231(02)00013-7
   Web of Science ®Google Scholar
• G.M. Kulikov and S.V. Plotnikova, Exact geometry piezoelectric solid-shell element based on the 7-parameter model, Mech. Adv. Mate. Struct 18 (2011), pp. 133–146. doi:10.1080/15376494.2010.496067
   Web of Science ®Google Scholar
• G.M. Kulikov and S.V. Plotnikova, A new approach to three-dimensional exact solutions for functionally graded piezoelectric laminated plates, Compo. Struct. 106 (2013), pp. 33–46. doi:10.1016/j.compstruct.2013.05.037
   Web of Science ®Google Scholar
• G. Rama, A 3-node piezoelectric shell element for linear and geometrically nonlinear dynamic analysis of smart structures, FACTA UNIVERSITATIS, Series: Mech. Eng 15 (1) (2017), pp. 31–44. doi:10.22190/FUME170225002R
   Web of Science ®Google Scholar
• D. Marinković and G. Rama, Co-rotational shell element for numerical analysis of laminated piezoelectric composite structures, Composites Part. B: Eng 125 (2017), pp. 144–156. doi:10.1016/j.compositesb.2017.05.061
   Web of Science ®Google Scholar
• T. Nestorović, S. Shabadi, D. Marinković, and M. Trajkov, Modeling of piezoelectric smart structures by implementation of a user defined shell finite element, FACTA UNIVERSITATIS, Series: Mech. Eng 11 (1) (2013), pp. 1–12.
   Google Scholar
• D. Marinković, H. Köppe, and U. Gabbert, Degenerated shell element for geometrically nonlinear analysis of thin-walled piezoelectric active structures, Smart Mater. Struct. 17 (1) (2008), pp. 015030. doi:10.1088/0964-1726/17/01/015030
   Google Scholar
• S. Gohari, S. Sharifi, and Z. Vrcelj, A novel explicit solution for twisting control of smart laminated cantilever composite plates and beams using inclined piezoelectric actuators, Compo. Struct. 161 (2017), pp. 477–504. doi:10.1016/j.compstruct.2016.11.063
   Web of Science ®Google Scholar
• C.S. Rekatsinas and D.A. Saravanos, A cubic spline layerwise time domain spectral FE for guided waves simulation in laminated composite plate structures with physically modeled active piezoelectric sensors, Int. J. Solids. Struct 24 (1) (2017), pp. 176-191.
   PubMed Web of Science ®Google Scholar
• Babushka, I., Chandra, J., & Flaherty, J. E. (Eds.). Adaptive Computational Methods for PartialDifferential Equations Vol. 16. Siam, Proceedings, College Park, PA, (1983).
   Google Scholar
• B.A. Szabo and I. Babuska, Finite Element Analysis, John Wiley & Sons, 1991.
   Google Scholar
• K.J. Bathe, Finite element procedure, Prentice Hall, 1996.
   Google Scholar
• D.M. Thompson and O.H. Jr Griffin, 2-D to 3-D global/local finite element analysis of cross-ply composite laminates, J. Reinforced Plas. Compos. 9 (1990), pp. 492–502. doi:10.1177/073168449000900506
   Web of Science ®Google Scholar
• K.M. Mao and C.T. Sun, A refined global-local finite element analysis method, Int. J. Numer. Methods Eng 32 (1991), pp. 29–43. doi:10.1002/(ISSN)1097-0207
   Web of Science ®Google Scholar
• J.D. Whitcomb and K. Woo, Application of iterative global/local finite element analysis. part 1: Linear analysis, Commun. Numer. Methods Eng 9 (9) (1993), pp. 745–756. doi:10.1002/cnm.1640090905
   Web of Science ®Google Scholar
• J.D. Whitcomb and K. Woo, Application of iterative global/local finite element analysis. Part 2: Geometrically non-linear analysis, Commun. Numer. Methods Eng 9 (9) (1993), pp. 757–766. doi:10.1002/cnm.1640090906
   Web of Science ®Google Scholar
• A. Pagani, S. Valvano, and E. Carrera, Analysis of laminated composites and sandwich structures by variable-kinematic MITC9 plate elements, J. Sandwich. Structures. Mater (2016). doi:10.1177/1099636216650988
   Google Scholar
• E. Carrera, A. Pagani, and S. Valvano, Shell elements with through-the-thickness variable kinematics for the analysis of laminated composite and sandwich structures, Composites Part B 111 (2017), pp. 294–314. doi:10.1016/j.compositesb.2016.12.001
   Web of Science ®Google Scholar
• E. Carrera and S. Valvano, A variable kinematic shell formulation applied to thermal stress of laminated structures, J. Thermal Stresses 40 (2017), pp. 803–827. doi:10.1080/01495739.2016.1253439
   Web of Science ®Google Scholar
• E. Carrera and S. Valvano, Analysis of laminated composite structures with embedded piezoelectric sheets by variable kinematic shell elements, J. Intell. Mater. Syst. Struct 28 (20) (2017), pp. 2959–2987. doi:10.1177/1045389X17704913
   Google Scholar
• F. Brezzi and L.D. Marini, The three-field formulation for elasticity problems, GAMM Mitteilungen 28 (2005), pp. 124–153. doi:10.1002/gamm.v28.2
   Google Scholar
• E. Carrera, A. Pagani, and M. Petrolo, Use of Lagrange multipliers to combine 1D variable kinematic finite elements, Comput. Struct. 129 (2013), pp. 194–206. doi:10.1016/j.compstruc.2013.07.005
   Web of Science ®Google Scholar
• H. Ben Dhia, Multiscale mechanical problems: The Arlequin method, Comptes Rendus De L Academie Des Sciences Series IIB Mechanics Physics Astronomy 326 (12) (1998), pp. 899–904.
   Google Scholar
• H. Ben Dhia, The Arlequin method as a flexible engineering tool, Int. J. Numer. Methods Eng 62 (11) (2005), pp. 1442–1462. doi:10.1002/nme.1229
   Web of Science ®Google Scholar
• H. Ben Dhia, Further insights by theoretical investigations of the multiscale Arlequin method, Int. J. Multiscale Computational Eng. 6 (3) (2008), pp. 215–232. doi:10.1615/IntJMultCompEng.v6.i3
   Web of Science ®Google Scholar
• H. Hu, S. Belouettar, M. Potier-Ferry, and E.M. Daya, Multi-scale modelling of sandwich structures using the Arlequin method. Part I: Linear modelling, Finite Elem. Anal. Des. 45 (1) (2008), pp. 37–51. doi:10.1016/j.finel.2008.07.003
   Web of Science ®Google Scholar
• H. Hu, S. Belouettar, M. Potier-Ferry, E.M. Daya, and A. Makradi, Multi-scale nonlinear modelling of sandwich structures using the Arlequin method, Finite Elem. Anal. Des. 92 (2) (2010), pp. 515–522.
   Google Scholar
• F. Biscani, G. Giunta, S. Belouettar, E. Carrera, and H. Hu, Variable kinematic beam elements coupled via Arlequin method, Compo. Struct. 93 (2) (2011), pp. 697–708. doi:10.1016/j.compstruct.2010.08.009
   Web of Science ®Google Scholar
• F. Biscani, G. Giunta, S. Belouettar, E. Carrera, and H. Hu, Variable kinematic plate elements coupled via Arlequin method, Int. J. Numer. Methods Eng 91 (2012), pp. 1264–1290. doi:10.1002/nme.v91.12
   Web of Science ®Google Scholar
• F. Biscani, P. Nali, S. Belouettar, and E. Carrera, Coupling of hierarchical piezoelectric plate finite elements via Arlequin method, J. Intell. Mater. Syst. Struct 23 (7) (2012), pp. 749–764. doi:10.1177/1045389X12437885
   Web of Science ®Google Scholar
• E. Carrera, S. Valvano, and G.M. Kulikov, Multilayered plate elements with node-dependent kinematics for electro-mechanical problems, Int. J. Smart Nano Mater. (In Press). doi:10.1080/19475411.2017.1376722
   Google Scholar
• E. Carrera, A. Pagani, and S. Valvano, Multilayered plate elements accounting for refined theories and node-dependent kinematics, Composites Part. B: Eng 114 (2017), pp. 189–210. doi:10.1016/j.compositesb.2017.01.022
   Web of Science ®Google Scholar
• S. Valvano and E. Carrera, Multilayered plate elements with node-dependent kinematics for the analysis of composite and sandwich structures, FACTA UNIVERSITATIS, Series: Mech. Eng 15 (1) (2017), pp. 1–30. doi:10.22190/FUME170315001V
   Web of Science ®Google Scholar
• K.J. Bathe and E. Dvorkin, A formulation of general shell elements - the use of mixed interpolation of tensorial components, Int. J. Numer. Methods Eng 22 (1986), pp. 697–722. doi:10.1002/nme.1620220312
   Web of Science ®Google Scholar
• K.J. Bathe and F. Brezzi, A simplified analysis of two plate bending elements-the MITC4 and MITC9 elements, Proceedings, Numerical Methods in Engineering: Theory and Applications, 1987.
   Google Scholar
• K.J. Bathe, F. Brezzi, and S.W. Cho, The MICT7 and MITC9 plate bending elements, Comput. Struct 32 (3–4) (1989), pp. 797–814. doi:10.1016/0045-7949(89)90365-9
   Web of Science ®Google Scholar
• M.L. Bucalem and E. Dvorkin, Higher-order MITC general shell elements, Int. J. Numer. Methods Eng 36 (1993), pp. 3729–3754. doi:10.1002/nme.1620362109
   Web of Science ®Google Scholar
• M. Cinefra, S. Valvano, and E. Carrera, Thermal stress analysis of laminated structures by a variable kinematic MITC9 shell element, J. Thermal Stresses 39 (2) (2016), pp. 121–141. doi:10.1080/01495739.2015.1123591
   Web of Science ®Google Scholar
• M. Cinefra, S. Valvano, and E. Carrera, A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches, Int. J. Smart Nano Mater. 6 (2) (2015), pp. 85–104. doi:10.1080/19475411.2015.1037377
   Web of Science ®Google Scholar
• E. Carrera, Theories and finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking, Arch. Computational Methods Eng. 10 (3) (2003), pp. 215–296. doi:10.1007/BF02736224
   Web of Science ®Google Scholar
• E. Carrera, Multilayered shell theories accounting for layerwise mixed description, Part 1: Governing equations, AIAA J. 37 (9) (1999), pp. 1107–1116. doi:10.2514/2.821
   Google Scholar
• E. Carrera, Multilayered shell theories accounting for layerwise mixed description, Part 2: Numerical evaluations, AIAA J. 37 (9) (1999), pp. 1117–1124. doi:10.2514/2.822
   Google Scholar
• J.N. Reddy, An evaluation of equivalent-single-layer and layerwise theories of composite laminates, Compo. Struct. 25 (1993), pp. 21–35. doi:10.1016/0263-8223(93)90147-I
   Web of Science ®Google Scholar
• E. Carrera, S. Brischetto, and P. Nali, Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis, John Wiley & Sons, 2011.
   Google Scholar
• E. Carrera, M. Cinefra, M. Petrolo, and E. Zappino, Finite Element Analysis of Structures through Unified Formulation, John Wiley & Sons, 2014.
   Google Scholar
• N.N. Rogacheva, The Theory of Piezoelectric Shells and Plates, CRC Press, Boca Raton, 1994.
   Google Scholar
• E. Carrera, S. Valvano, and G.M. Kulikov, Global-Local Analysis of Composite and Sandwich Multilayered Structures by Shell Elements with Node-Dependent Kinematics. To be submitted.
   Google Scholar
• H. Kioua and S. Mirza, Piezoelectric induced bending and twisting of laminated composite shallow shells, Smart Mater. Struct. 9 (2000), pp. 476–484. doi:10.1088/0964-1726/9/4/310
   Web of Science ®Google Scholar
• F. Kpeky, F. Abed-Meraim, H. Boudaoud, and E.M. Daya, Linear and quadratic solidshell finite elements SHB8PSE and SHB20E for the modeling of piezoelectric sandwich structures, Mech. Adv. Mate. Struct (2017), pp. 1–20. doi:10.1080/15376494.2017.1285466.
   Google Scholar
• C.T. Sun and X.D. Zhang, Use of thickness-shear mode in adaptive sandwich structures, Smart Mater. Struct. 4 (1995), pp. 202–206. doi:10.1088/0964-1726/4/3/007
   Web of Science ®Google Scholar