5.9 Summary
99
5.9 Summary
This chapter developed static and dynamic nonlinear FE models for piezoelectric
integrated smart structures undergoing large displacements and under strong electric
fields. In the FE models, both linear piezoelectric constitutive equations and electroelastic nonlinear constitutive equations were considered, where electric field through
the thickness are assumed constant. Four types of shell elements were developed for
composite or piezoelectric laminated thin-walled structures. Various geometrically
nonlinear strain-displacement relations were included in the FE models. In LRT56
FE models, Euler angles were used to represent unrestricted finite rotations in shell
structures. In the end of this chapter, several numerical algorithms for solving static
and dynamic equations were discussed.
References
1. L. Librescu, Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures
(Noordhoff International, Leyden, 1975)
2. S.Q. Zhang, R. Schmidt, Large rotation theory for static analysis of composite and piezoelectric
laminated thin-walled structures. Thin-Walled Struct. 78, 16–25 (2014)
3. S.Q. Zhang, R. Schmidt, Large rotation FE transient analysis of piezolaminated thin-walled
smart structures. Smart Mater. Struct. 22, 105025 (2013)
4. I. Kreja, R. Schmidt, Large rotations in first-order shear deformation FE analysis of laminated
shells. Int. J. Non-Linear Mech. 41, 101–123 (2006)
5. G.A. Korn, T.M. Korn, Mathematical Handbook for Scientists and Engineers (Dover Publication Inc., Mineola, New York, 2000)
6. K.J. Bathe, Finite Element Procedures (Prentice Hall, New Jersey, 1996)
7. O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6th edn. (Butterworth-Heinemann, Oxford, 2005)
8. I. Kreja, Geometrically non-linear analysis of layered composite plates and shells. Habilitation
Thesis, Published as Monografie 83, Politechnika Gda´ nska (2007)
9. V. Piefort, Finite element modeling of piezoelectric active structures. Ph.D. Thesis, Universite
Libre de Bruxelles (2001)
10. D.T. Vu, Geometrically nonlinear higher-oder shear deformation FE analysis of thin-walled
smart structures. Ph.D. Thesis, RWTH Aachen University (2011)
11. S. Lentzen, Nonlinear coupled thermopiezoelectric modelling and FE-simulation of smart
structures. Ph.D. Thesis, RWTH Aachen University, in: Fortschritt-Berichte VDI, Reihe 20,
Nr. 419, VDI Verlag, Düsseldorf (2009)
12. M.A. Crisfield, Non-linear Finite Element Analysis of Solids and Structures (Wiley, 1991)
13. I. Chowdhury, S.P. Dasgupta, Computation of Rayleigh damping coefficients for large systems.
Electron. J. Geotech. Eng. 8, 10392376 (2003)
14. S.Q. Zhang, G.Z. Zhao, S.Y. Zhang, R. Schmidt, X.S. Qin, Geometrically nonlinear FE analysis
of piezoelectric laminated composite structures under strong driving electric field. Compos.
Struct. 181, 112–120 (2017)
15. C.L. Liao, J.N. Reddy, An Incremental Total Lagrangian Formulation for General Anisotropic
Shell-Type Structures (Virginia Polytechnic Institute and State University, Blacksburg, Virginia,
1987)
99
5.9 Summary
This chapter developed static and dynamic nonlinear FE models for piezoelectric
integrated smart structures undergoing large displacements and under strong electric
fields. In the FE models, both linear piezoelectric constitutive equations and electroelastic nonlinear constitutive equations were considered, where electric field through
the thickness are assumed constant. Four types of shell elements were developed for
composite or piezoelectric laminated thin-walled structures. Various geometrically
nonlinear strain-displacement relations were included in the FE models. In LRT56
FE models, Euler angles were used to represent unrestricted finite rotations in shell
structures. In the end of this chapter, several numerical algorithms for solving static
and dynamic equations were discussed.
References
1. L. Librescu, Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures
(Noordhoff International, Leyden, 1975)
2. S.Q. Zhang, R. Schmidt, Large rotation theory for static analysis of composite and piezoelectric
laminated thin-walled structures. Thin-Walled Struct. 78, 16–25 (2014)
3. S.Q. Zhang, R. Schmidt, Large rotation FE transient analysis of piezolaminated thin-walled
smart structures. Smart Mater. Struct. 22, 105025 (2013)
4. I. Kreja, R. Schmidt, Large rotations in first-order shear deformation FE analysis of laminated
shells. Int. J. Non-Linear Mech. 41, 101–123 (2006)
5. G.A. Korn, T.M. Korn, Mathematical Handbook for Scientists and Engineers (Dover Publication Inc., Mineola, New York, 2000)
6. K.J. Bathe, Finite Element Procedures (Prentice Hall, New Jersey, 1996)
7. O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6th edn. (Butterworth-Heinemann, Oxford, 2005)
8. I. Kreja, Geometrically non-linear analysis of layered composite plates and shells. Habilitation
Thesis, Published as Monografie 83, Politechnika Gda´ nska (2007)
9. V. Piefort, Finite element modeling of piezoelectric active structures. Ph.D. Thesis, Universite
Libre de Bruxelles (2001)
10. D.T. Vu, Geometrically nonlinear higher-oder shear deformation FE analysis of thin-walled
smart structures. Ph.D. Thesis, RWTH Aachen University (2011)
11. S. Lentzen, Nonlinear coupled thermopiezoelectric modelling and FE-simulation of smart
structures. Ph.D. Thesis, RWTH Aachen University, in: Fortschritt-Berichte VDI, Reihe 20,
Nr. 419, VDI Verlag, Düsseldorf (2009)
12. M.A. Crisfield, Non-linear Finite Element Analysis of Solids and Structures (Wiley, 1991)
13. I. Chowdhury, S.P. Dasgupta, Computation of Rayleigh damping coefficients for large systems.
Electron. J. Geotech. Eng. 8, 10392376 (2003)
14. S.Q. Zhang, G.Z. Zhao, S.Y. Zhang, R. Schmidt, X.S. Qin, Geometrically nonlinear FE analysis
of piezoelectric laminated composite structures under strong driving electric field. Compos.
Struct. 181, 112–120 (2017)
15. C.L. Liao, J.N. Reddy, An Incremental Total Lagrangian Formulation for General Anisotropic
Shell-Type Structures (Virginia Polytechnic Institute and State University, Blacksburg, Virginia,
1987)