6.4 Electroelastic Nonlinear Analysis of Smart Structures
135
in this example). For extremely large electric field (>800 V/mm), the LRT56SE
curves deviate dramatically from other curves, especially for the radial displacements. This is because the structure undergoes large displacements and rotations.
LRT56SE model considers both the electroelastic nonlinearity and full geometric
nonlinearity with large rotations.
6.5 Summary
This chapter dealt with nonlinear simulations of composite and smart structures. The
present geometrically nonlinear models, RVK5, MRT5, LRT5 and LRT56, were first
validated by static analysis and buckling analysis of composite laminated thin-walled
structures. Later, the geometrically nonlinear models were applied to numerical analysis of piezolaminated beams, plates and shells. In the final part, the simulation of both
geometrically and electroelastic materially nonlinear phenomena were performed on
piezoelectric integrated smart structures.
References
1. C.T. Sun, H. Chin, Analysis of asymmetric composite laminates. AIAA J. 26, 714–718 (1988)
2. J.N. Reddy, On refined computational models of composite laminates. Int. J. Numer. Methods
Eng. 27, 361–382 (1989)
3. Y. Basar, Y. Ding, R. Schultz, Refined shear-deformation models for composite laminates with
finite rotations. Int. J. Solids Struct. 30, 2611–2638 (1993)
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. 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)
6. S.Q. Zhang, R. Schmidt, Static and dynamic FE analysis of piezoelectric integrated thin-walled
composite structures with large rotations. Compos. Struct. 112, 345–357 (2014)
7. N. Stander, A. Matzenmiller, E. Ramm, An assessment of assumed strain methods in finite
rotation shell analysis. Eng. Comput. 6, 58–66 (1989)
8. A.F. Saleeb, T.Y. Chang, W. Graf, S. Yingyeunyong, A hybrid/mixed model for non-linear
shell analysis and its applications to large-rotation problems. Int. J. Numer. Methods Eng. 29,
407–446 (1990)
9. C. Sansour, H. Bufler, An exact finite rotation shell theory, its mixed variational formulation
and its finite element implementation. Int. J. Numer. Methods Eng. 34, 73–115 (1992)
10. L. Jiang, M.W. Chernuka, A simple four-noded corotational shell element for arbitrarily large
rotations. Comput. Struct. 53, 1123–1132 (1994)
11. A. Masud, C.L. Tham, W.K. Liu, A stabilized 3-D co-rotational formulation for geometrically
nonlinear analysis of multi-layered composite shells. Comput. Mech. 26, 1–12 (2000)
12. K.Y. Sze, X.H. Liu, S.H. Lo, Popular benchmark problems for geometric nonlinear analysis of
shells. Finite Elem. Anal. Des. 40, 1551–1569 (2004)
13. R.A. Arciniega, J.N. Reddy, Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures. Comput. Methods Appl. Mech. Eng. 196, 1048–1073 (2007)
14. S. Saigal, R.K. Kapania, T.Y. Yang, Geometrically nonlinear finite element analysis of imperfect
laminated shells. J. Compos. Mater. 20, 197–214 (1986)
135
in this example). For extremely large electric field (>800 V/mm), the LRT56SE
curves deviate dramatically from other curves, especially for the radial displacements. This is because the structure undergoes large displacements and rotations.
LRT56SE model considers both the electroelastic nonlinearity and full geometric
nonlinearity with large rotations.
6.5 Summary
This chapter dealt with nonlinear simulations of composite and smart structures. The
present geometrically nonlinear models, RVK5, MRT5, LRT5 and LRT56, were first
validated by static analysis and buckling analysis of composite laminated thin-walled
structures. Later, the geometrically nonlinear models were applied to numerical analysis of piezolaminated beams, plates and shells. In the final part, the simulation of both
geometrically and electroelastic materially nonlinear phenomena were performed on
piezoelectric integrated smart structures.
References
1. C.T. Sun, H. Chin, Analysis of asymmetric composite laminates. AIAA J. 26, 714–718 (1988)
2. J.N. Reddy, On refined computational models of composite laminates. Int. J. Numer. Methods
Eng. 27, 361–382 (1989)
3. Y. Basar, Y. Ding, R. Schultz, Refined shear-deformation models for composite laminates with
finite rotations. Int. J. Solids Struct. 30, 2611–2638 (1993)
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. 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)
6. S.Q. Zhang, R. Schmidt, Static and dynamic FE analysis of piezoelectric integrated thin-walled
composite structures with large rotations. Compos. Struct. 112, 345–357 (2014)
7. N. Stander, A. Matzenmiller, E. Ramm, An assessment of assumed strain methods in finite
rotation shell analysis. Eng. Comput. 6, 58–66 (1989)
8. A.F. Saleeb, T.Y. Chang, W. Graf, S. Yingyeunyong, A hybrid/mixed model for non-linear
shell analysis and its applications to large-rotation problems. Int. J. Numer. Methods Eng. 29,
407–446 (1990)
9. C. Sansour, H. Bufler, An exact finite rotation shell theory, its mixed variational formulation
and its finite element implementation. Int. J. Numer. Methods Eng. 34, 73–115 (1992)
10. L. Jiang, M.W. Chernuka, A simple four-noded corotational shell element for arbitrarily large
rotations. Comput. Struct. 53, 1123–1132 (1994)
11. A. Masud, C.L. Tham, W.K. Liu, A stabilized 3-D co-rotational formulation for geometrically
nonlinear analysis of multi-layered composite shells. Comput. Mech. 26, 1–12 (2000)
12. K.Y. Sze, X.H. Liu, S.H. Lo, Popular benchmark problems for geometric nonlinear analysis of
shells. Finite Elem. Anal. Des. 40, 1551–1569 (2004)
13. R.A. Arciniega, J.N. Reddy, Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures. Comput. Methods Appl. Mech. Eng. 196, 1048–1073 (2007)
14. S. Saigal, R.K. Kapania, T.Y. Yang, Geometrically nonlinear finite element analysis of imperfect
laminated shells. J. Compos. Mater. 20, 197–214 (1986)