Mixed piezoelectric plate elements with continuous transverse electric displacements

Journal of Mechanics of Materials and Structures

Volumn 2, Issue 3, 2007, Pages 421-438

  Carrera, Erasmo ^a   Fagiano, Christian ^a,b  

^a POLITECNICO DI TORINO   (Italy)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Finite elements; Mixed method; Piezoelectric plates; Transverse continuity; Unified formulation

Indexed keywords

EID: 34548656858     PISSN: 15593959     EISSN: None     Source Type: Journal    
DOI: 10.2140/jomms.2007.2.421     Document Type: Article

References (41)

1. [Auricchio et al. 2001] F. Auricchio, P. Bisegna, and C. Lovadina, "Finite element approximation of piezoelectric plates", Int. J. Numer. Methods Eng. 50:6 (2001), 1469-1499.
2. [Ballhause et al. 2005] D. Ballhause, M. D'Ottavio, B. Kröplin, and E. Carrera, "A unified formulation to assess multilayered theories for piezoelectric plates", Comput. Struct. 83:15-16 (2005), 1217-1235.
3. [Batra and Vidoli 2002] R. C. Batra and S. Vidoli, "Higher-order piezoelectric plate theory derived from a three-dimensional variational principle", AIAA J. 40:1 (2002), 91-104.
4. [Benjeddou 2000] A. Benjeddou, "Advances in piezoelectric finite element modeling of adaptive structural elements: a survey", Comput. Struct. 76:1-3 (2000), 347-363.
5. [Carrera 1995] E. Carrera, "A class of two dimensional theories for multilayered plates analysis", Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 19-20 (1995), 49-87.
6. 0 Reissner-Mindlin multilayered plate elements including zig-zag and interlaminar stresses continuity", Int. J. Numer. Methods Eng. 39:11 (1996), 1797-1820.
7. [Carrera 1997] E. Carrera, "An improved Reissner-Mindlin type element for the electromechanical analysis of multilayered plates including piezo layers", J. Intell. Mater. Syst. Struct. 8:3 (1997), 232-248.
8. [Carrera 1999a] E. Carrera, "A Reissner's mixed variational theorem applied to vibrational analysis of multilayered shell", J. Appl. Mech. (ASME) 66:1 (1999), 69-78.
9. [Carrera 1999b] E. Carrera, "A study of transverse normal stress effects on vibration of multilayered plates and shells". J. Sound Vib. 225:5 (1999), 803-829.
10. [Carrera 2001] E. Carrera, "Developments, ideas, and evaluations based upon Reissher's mixed variational theorem in the modeling of multilayered plates and shells", Appl. Mech. Rev. 54:4 (2001), 301-329.
11. [Carrera 2003a] E. Carrera, "Historical review of zig-zag theories for multilayered plates and shell", Appl. Mech. Rev. 56:3 (2003), 287-308.
12. [Carrera 2003b] E. Carrera, "Theories and finite elements for multilayered plates and-shells: a unified compact formulation with numerical assessment and benchmarking", Arch. Comput. Methods Eng. 10:3 (2003), 215-296. Zbl 02097772
13. [Carrera and Boscolo 2006] E. Carrera and M. Boscolo, "Classical and mixed finite-elements for static and dynamics analysis of piezoelectric plates", Int. J. Numer. Methods Eng. (2006). Published online 6 Nov 2006.
14. [Carrera and DeMasi 2002a] E. Carrera and L. DeMasi, "Classical and advanced multilayered plate elements based upon PVD and RMVT, 1: Derivation of finite element matrices", Int. J. Numer. Methods Eng. 55:2 (2002), 191-231.
15. [Carrera and DeMasi 2002b] E. Carrera and L. DeMasi, "Classical and advanced multilayered plate elements based upon PVD and RMVT, 2: Numerical implementations". Int. J. Numer. Methods Eng. 55:3 (2002), 253-291.
16. [Carrera et al. 2005] E. Carrera, S. Brischetto, and M. D'Ottavio, "Vibrations of piezoelectric shells by unified formulations in the Reissner's mixed theorem", in SMART '05: Second ECCOMAS Thematic Conference on Smart Structures and Materials (Lisbon), edited by C. A. Mota Soares et al., 2005.
17. [Chopra 1996] I. Chopra, "Review of current status of smart structures and integrated systems", pp. 20-62 in Smart structures and materials 1996: Smart structures and integrated systems (San Diego, CA), edited by I. Chopra, Proceedings of SPIE 2717, SPIE, Bellingham, WA, 1996.
18. [Chopra 2002] I. Chopra, "Review of state of art of smart structures and integrated systems", AIAA J. 40:11 (2002), 2145-2187.
19. [Crawley and de Luis 1987] E. F. Crawley and J. de Luis, "Use of piezoelectric actuators as elements of intelligent structures", AIAA J. 25:10 (1987), 1373-1385.
20. [D'Ottavio and Kröplin 2006] M. D'Ottavio and B. Kröplin, "An extension of Reissner mixed variational theorem to piezoelectric laminates", Mech. Adv. Mater. Struct. 13:2 (2006), 139-150.
21. [Garcia Lage et al. 2004a] R. Garcia Lage, C. M. Mota Soares, C. A. Mota Soares, and J. N. Reddy, "Layerwise partial mixed finite element analysis of magneto-electro-elastic plates", Comput. Struct. 82:17-19 (2004), 1293-1301.
22. [Garcia Lage et al. 2004b] R. Garcia Lage, C. M. Mota Soares, C. A. Mota Soares, and J. N. Reddy, "Modeling of piezo-laminated plates using layer-wise mixed finite elements", Comput. Struct. 82:23-26 (2004), 1849-1863.
23. [Heyliger 1994] P. Heyliger, "Static behavior of laminated elastic/ piezoelectric plates", AIAA J. 32:12 (1994), 2481-2484.
24. [Heyliger and Saravanos 1995] P. Heyliger and D. A. Saravanos, "Exact free-vibration analysis of laminated plates with embeded piezoelectric layers", J. Acoust. Soc. Am. 98:3 (1995), 1547-1557.
25. [Ikeda 1996] T. Ikeda, Fundamentals of piezoelectricity, corrected ed., Oxford University Press, New York, 1996.
26. [Kögl and Bucalem 2005a] M. Kögl and M. L. Bucalem, "Analysis of smart laminates using piezoelectric MITC plate and shell elements", Comput. Struct. 83:15-16 (2005), 1153-1163.
27. [Kögl and Bucalem 2005b] M. Kögl and M. L. Bucalem, "A family of piezoelectric MITC plate elements", Comput. Struct. 83:15-16 (2005), 1277-1297.
28. [Lee 1990] C. K. Lee, "Theory of laminated piezolectric plates for the design of distributed sensors/actuators, I: Governing equations and reciprocal relationships", J. Acoust. Soc. Am 87:3 (1990), 1144-1158.
29. [Mitchell and Reddy 1995] J. A. Mitchell and J. N. Reddy, "High frequency vibrations of piezoelectric cristal plates", Int. J. Solids Struct. 32:16 (1995), 2345-2367.
30. [Oh and Cho 2004] J. Oh and M. Cho, "A finite element based on cubic zig-zag plate theory for the prediction of thermo-electric-mechanical behaviors", Int. J. Solids Struct. 41:5-6 (2004), 1357-1375. In press.
31. [Reissner 1984] E. Reissner, "On a certain mixed variational theory and a proposed application", Int. J. Numer. Methods Eng. 20:7 (1984), 1366-1368.
32. [Robbins and Reddy 1991] D. H. Robbins and J. N. Reddy, "Analysis of piezolectric actuated-beams using a layer-wise-displacements theory", Comput. Struct. 41:2 (1991), 265-279.
33. [Saravanos and Heyliger 1999] D. A. Saravanos and P. R. Heyliger, "Mechanics and computational models for laminated piezoelectric beams, plates, and shells", Appl. Mech. Rev. 52:10 (1999), 305-320.
34. [Sheikh et al. 2001] A. H. Sheikh, P. Topdar, and S. Halder, "An appropriate fe model for through-thickness variation of displacement and potential in thin moderately thick smart laminates", Compos. Struct. 51:4 (2001), 401-409.
35. [Shu 2005] X. Shu, "Free-vibration of laminated piezoelectric composite plates based on an accurate theory", Compos. Struct. 67:4 (2005), 375-382.
36. [Thornbuegh and Chattopadhyay 2002] R. P. Thornbuegh and A. Chattopadhyay, "Simultaneous modeling of mechanical and electrical response of smart composite structures", AIAA J. 40:8 (2002), 1603-1610.
37. [Tiersten 1969] H. F. Tiersten, Linear piezoelectric plate vibrations, Plenum Press, New York, 1969.
38. [Vidoli and Batra 2000] S. Vidoli and R. C. Batra, "Derivation of plate and rod equations for a piezolectric body from a mixed three-dimensional variational principle", J. Elasticity 59:1-3 (2000), 23-50.
39. [Wang and Yang 2000] J. Wang and J. Yang, "High-order theories of piezoelectric plates and applications", Appl. Mech. Rev. 53:4 (2000), 87-96.
40. [Wang et al. 1997] J. Wang, Y.-K. Yong, and T. Imai, "Finite element analysis of the piezoelectric vibrations of quartz plate resonators with higher-order plate theory" pp. 650-658 in Proceedings of the 1997 IEEE International Frequency Control Symposium (Orlando, FL), IEEE New York, 1997.
41. [Yang and Batra 1995] J. S. Yang and R. C. Batra, "Mixed variational principles in non-linear electroelasticity", Int. J. Non-Linear Mech. 30:5 (1995), 719-725.