Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration control

International Journal for Numerical Methods in Engineering

Volumn 64, Issue 15, 2005, Pages 1981-2013

  Tan, X G ^a,b   Vu Quoc, L ^a  

^a UNIVERSITY OF FLORIDA   (United States)

^b CFD RESEARCH CORPORATION   (United States)

Author keywords

Active vibration control; Composite shell; Coupled field problem; Dynamic analyses; Finite strains; Large deformation; Multilayer; Piezoelectric patch; Solid shell element

Indexed keywords

COMPUTER SIMULATION; DEFORMATION; DEGREES OF FREEDOM (MECHANICS); PIEZOELECTRIC DEVICES; SHELLS (STRUCTURES); STRAIN; VARIATIONAL TECHNIQUES; VIBRATION CONTROL;

ACTIVE VIBRATION CONTROL; COUPLED-FIELD PROBLEM; DYNAMIC ANALYSES; FINITE STRAINS; LARGE DEFORMATION; PIEZOELECTRIC PATCH; SOLID SHELL ELEMENT;

COMPOSITE STRUCTURES;

COMPOSITE; DEFORMATION; PIEZOELECTRICITY;

EID: 28844499528     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1433     Document Type: Article

References (54)

1. Berger H, Gabbert U, Koppe H, Seeger F. Finite element analysis and design of piezoelectric controlled smart structures. Journal of Theoretical and Applied Mechanics 2000; 38(3):475-498.
2. Balamurugan V, Narayanan S. Active vibration control of smart shells using distributed piezoelectric sensors and actuators. Smart Materials and Structures 2001; 10(2):173-180.
3. Gabbert U. Koppe H. Seeger F. Overall design of actively controlled smart structures by the finite element method. Proceedings of the SPIE - The International Society for Optical Engineering, vol. 4326, 2001; 113-122.
4. Lim Y-H, Gopinathan SV, Varadan VV, Varadan VK. Finite element simulation of smart structures using an optimal output feedback controlled for vibration and noise control. Smart Materials and Structures 1999; 8(3):324-337.
5. Thirupathi SR, Seshu P, Naganathan NG. A finite-element static analysis of smart turbine blades. Smart Materials and Structures 1997; 6(5):607-615.
6. Loewy RG. Recent developments in smart structures with aeronautical applications. Smart Materials and Structures 1997; 6(5):11-42.
7. Chopra I. Review of current status of smart structures and integrated systems. Proceedings of SPIE - The International Society for Optical Engineering, vol. 2717, 1996; 20-62. Smart Structures and Materials 1996: Smart Structures and Integrated Systems, San Diego, CA, U.S.A.
8. Chee CYK, Tong L, Steven GP. Review on the modelling of piezoelectric sensors and actuators incorporated in intelligent structures. Journal of Intelligent Material Systems and Structures 1998; 9(1):3-19.
9. Sunar M, Rao SS. Recent advances in sensing and control of flexible structures via piezoelectric materials technology. Applied Mechanics Review 1999; 52(1):1-16.
10. Benjeddou A. Advances in piezoelectric finite element modeling of adaptive structural elements: a survey. Computers and Structures 2000; 76(1-3):347-363.
11. Niezrecki C. Brei D, Balakrishnan S, Moskalik A. Piezoelectric actuation: state of the art. Shock and Vibration Digest 2001; 33(4):269-280.
12. Hwang WS, Park HC. Finite element modeling of piezoelectric sensors and actuators. AIAA Journal 1993; 31(5):930-937.
13. Detwiler DT, Shen MHH, Venkayya VB. Finite element analysis of laminated composite structures containing distributed piezoelectric actuators and sensors. Finite Elements in Analysis and Design 1995; 20(2):87-100.
14. Balamurugan V, Narayanan S. Shell finite element for smart piezoelectric composite plate/shell structures and its application to the study of active vibration control. Finite Elements in Analysis and Design 2001; 37(9):713-738.
15. Gopinathan SV, Varadan VV, Varadan VK. Review and critique of theories for piezoelectric laminates. Smart Materials and Structures 2000; 9(1):24-48.
16. Correia VMF, Gomes MAA, Suleman A, Soares CMM, Soares CAM. Modelling and design of adaptive composite structures. Computer Methods in Applied Mechanics and Engineering 2000; 185:325-346.
17. Tzou HS, Ye R. Analysis of piezoelastic structures with laminated piezoelectric triangle shell elements. AIAA Journal 1996; 34(1):110-115.
18. Saravanos DA. Mixed laminated theory and finite element for smart piezoelectric composite shell structures. AIAA Journal 1997; 35(8):1327-1333.
19. Fox DD. Transverse shear and normal stresses in nonlinear shell theory. Computers and Structures 2000; 75:313-319.
20. Vu-Quoc L, Deng H, Tan XG. Geometrically-exact sandwich shells: the static case. Computer Methods in Applied Mechanics and Engineering 2000; 189(1):167-203.
21. Ghandi KM, Hagood NW. Nonlinear finite element modeling of phase transitions in electromechanically coupled material. In Smart Structures and Materials 1997: Mathematics and Control in Smart Structures, Varadan VV, Chandra J (eds). Proceedings of the SPIE Conference, San Diego, CA, SPIE - The International Society for Optical Engineering, vol. 2715, Bellingham, WA, 1997; 121-140.
22. Kamlah M, Tsakmakis C. Phenomenological modeling of the non-linear electro-mechanical coupling in ferroelectrics. International Journal of Solids and Structures 1999; 36(5):669-695.
23. Kamlah M, Bohle U. Finite element analysis of piezoceramic components taking into account ferroelectric hysteresis behaviour. International Journal of Solids and Structures 2001; 38:605-633.
24. Koko TS, Smith MJ, Orisamolu IR. Modeling stresses in piezoelectric smart structures under combined thermal and mechanical excitations. In Smart Structures and Materials 1999: Mathematics and Control in Smart Structures, Varadan VV (ed.), Proceedings of the SPIE Conference, vol. 3667, Newport Beach, CA. SPIE - The International Society for Optical Engineering, Bellingham, WA, 1999; 474-485.
25. Ha SK, Keilers C, Chang FK. Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators. AIAA Journal 1992; 30(3):772-780.
26. Panahandeh M, Cui YL, Kasper EP. Simulation of coupled systems in smart structures. In Smart Structures and Materials 1999: Mathematics and Control in Smart Structures, Varadan VV (ed.), Proceedings of the SPIE Conference, vol. 3039, Newport Beach, CA, SPIE - The International Society for Optical Engineering, Bellingham, WA, 1999; 292-304.
27. Vu-Quoc L, Tan XG. Optimal solid shells for non-linear analyses of multilayer composites. I. Statics. Computer Methods in Applied Mechanics and Engineering 2003; 192(9-10):975-1016.
28. Kim J, Varadan VV, Varadan VK. Finite element modelling of structures including piezoelectric active devices. International Journal for Numerical Methods in Engineering 1997; 40(5):817-832.
29. Sze KY, Yao LQ, Yi S. A hybrid stress ans solid-shell element and its generalization for smart structure modelling. II. Smart structure modelling. International Journal for Numerical Methods in Engineering 2000; 48(4):565-582.
30. Zienkiewicz OC, Taylor RL. The Finite Element Method, Volume 1: The Basis (5th edn). Butterworth-Heinemann: Oxford, 2000.
31. Simo, JC, Kennedy JG, Taylor RL. Complementary mixed finite element formulations for elastoplasticity. Computer Methods in Applied Mechanics and Engineering 1989; 74(2):177-206.
32. Vu-Quoc L, Tan XG. Optimal solid shells for non-linear analyses of multilayer composites. II. Dynamics, Computer Methods in Applied Mechanics and Engineering 2003b; 192(9-10):1017-1059.
33. Tan XG, Vu-Quoc L. Efficient and accurate multilayer solid-shell element: nonlinear materials at finite strain. International Journal for Numerical Methods in Engineering 2005; 63(15):2124-2170.
34. Dvorkin EN, Bathe K-J. Continuum mechanics based four-node shell element for general non-linear analysis. Engineering Computations 1984; 1(1):77-88.
35. Betsch P, Stein E. An assumed strain approach avoiding artificial thickness straining for a non-linear 4-node shell element. Communications in Numerical Methods in Engineering 1995; 11:899-909.
36. Wilson EL, Yuan MW, Dickens JM. Dynamic analysis by direct superposition of ritz vectors. Earthquake Engineering and Structural Dynamics 1982; 10(6):813-821.
37. Leger P. The use of load dependent vectors for dynamic and earthquake analyses. Ph.D. Thesis, University of California at Berkeley, Berkeley, CA, 1986.
38. Parlett BN. The Symmetric Eigenvalue Problem. Prentice-Hall: Englewood Cliffs, NJ, 1998.
39. Hughes TJR. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: New York, 1987.
40. Vu-Quoc L, Tan XG, Zhai Y. Quaterly reports on model reduction techniques for MEMS simulations. Technical Report, Aerospace Engineering, Mechanics Engineering Science, University of Florida, Gainesville, FL, 32611. BAA 97-17: DARPA Composite CAD Program, 1998-2000.
41. Anderson BDO, Moore JB. Optimal Control: Linear Quadratic Methods. Prentice-Hall: Englewood Cliffs, NJ, 1990.
42. Boyd SP, Barratt CH. Linear Controller Design: Limits of Performance. Prentice-Hall: Englewood Cliffs, NJ, 1991.
43. Meirovitch L. Dynamics and Control of Structures. Wiley: New York, 1990.
44. Taylor RL, Beresford PJ, Wilson EL. A non-conforming element for stress analysis. International Journal for Numerical Methods in Engineering 1976; 10:1211-1219.
45. Hoit M, Krishnamurthy K. 14-point reduced integration scheme for solid elements. Computers and Structures 1995; 54(4):725-730.
46. Irons BM. Quadrature rules for brick based finite elements. International Journal for Numerical Methods in Engineering 1971; 3:293-294.
47. Basar Y, Ding Y, Schultz R. Refined shear-deformation models for composite laminates with finite rotations. International Journal of Solids and Structures 1993; 30(19):2611-2638.
48. Andersson J, Sjogren S. Proper orthogonal decomposition: method and application on linear and non-linear models with piezoelectric materials. Master's Thesis, University of Florida, Gainesville, FL, 2001.
49. Crawley EF, Lazarus KB. Induced strain actuation of isotropic and anisotropic plates. AIAA Journal 1991; 29(6):944-951.
50. Saravanos DA, Heyliger PR, Hopkins DA. Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates. International Journal of Solids and Structures 1997; 34(3):359-378.
51. Hong SY. An optimally integrated four-node quadrilateral plate bending element. Ph.D. Thesis, The Pennsylvania State University, 1992.
52. Correiaa VMF, Soares CMM, Soares CAM. Refined models for the optimal design of adaptive structures using simulated annealing. Composite Structures 2001; 54(2-3):161-167.
53. Han J-H, Lee I. Optimal placement of piezoelectric sensors and actuators for vibration control of a composite plate using genetic algorithms. Smart Materials and Structures 1999; 8(2):257-267.
54. Gürdal Z, Haftka RT, Hajela P. Design and Optimization of Laminated Composite Materials. Wiley: New York, 1999.