THE USE OF AUXETIC MATERIALS IN SMART STRUCTURES
Hadjigeorgiou E. P. 1, Stavroulakis G. E. 2,3*
1 Department of Materials Science and Engineering, University of Ioannina, GR-45110 Ioannina, Greece
2 Department of Matematics, University of Ioannina, GR-45110Ioannina, Greece
3 Department of Civil Engineering, Technical University of Braunschweig, Germany
Received:
Rec. 14 December 2004
DOI: 10.12921/cmst.2004.10.02.147-160
OAI: oai:lib.psnc.pl:567
Abstract:
This paper presents a study of the implications of using auxetic materials in the design of
smart structures. By using auxetic materials as core and piezoelectric actuators as face layers to provide control forces, the problem of the shape control of sandwich beams is analyzed under loading conditions. The mechanical model is based on the shear deformable theory for beams and the linear theory of piezoelectricity. The numerical solution of the model is based on superconvergent (locking-free) finite elements for the beam theory, using Hamilton’s principle. The optimal voltages of the piezo-actuators for shape control of a cantilever beams with classical and auxetic material are determined by using a genetic optimization procedure. Related numerical solutions of static problems demonstrate the role of auxetic material in the deformation, shape control and stress distribution of the beam and related twodimensional
composite elastic structures.
Key words:
Auxetic materials, finite element analysis, genetic optimization., shape control, smart beams and plates
References:
[1] H. Janocha (Ed.), Adaptronics and Smart Structures, Springer-Verlag Berlin (1999).
[2] P. Gaudenzi, F. Enrico, V. Koumousis, and C. Gantes, Shape control of statically indeterminate lami nated beams with piezoelectric actuators. J. Intell. Mater. Syst. 9, 291-300 (1998).
[3] B. N. Agrawal and K E. Treanor, Shape control of statically indeterminate laminated beams with piezoelectric actuators. Smart Mater. Struct. 8, 729-740 (1999).
[4] C. Chee, L. Tong, and G. Steven, A buildup voltage (BVD) algorithm for shape control of smart plate structures. Engineering Structures 24, 5-11 (2000).
[5] H. Irschik, A review on static and dynamic shape control of structures using piezoelectric
actuation. Computational Mechanics 26, 115-128 (2002).
[6] E. P. Hadjigeorgiou, G. Foutsitzi, and G. E. Stavroulakis, Shape control of beams with piezo
electric actuators Proc. 6th Hellenic-European Conference on Computer Mathematics and its
Applications 25-27 September Athens HERCMA 2003, E. A. Lipitakis (Editor), LEA Publishers,
Vol. I, pp. 164-168 (2003).
[7] Z. Friedman and J. B. Kosmatka, An inproved two-node Timoshenko beam finite element. Comput. Struct. 47 473-481 (1993).
[8] J. N. Reddy, On locking-free shear deformable beam finite elements. Comput. Methods Appl. Mech. Engrg. 149 113-132 (1997).
[9] W. Yang, Z. M. Li, W. Shi, B. H. Xie, and M. B. Yang. On auxetic materials. J. Mater. Sci. 39,
3269-3279 (2004).
[10] T. Matsuoka, S. Yamamoto, and M. Takahara, Prediction of structures and mechanical properties of composites using genetic algorithm andfinite element method. J. Mater. Sci. 36, 27-33 (2001).
[11] K E. Evans and A. Alderson, Auxetic materials: Functional materials and structures from lateral thinking. Adv. Mater. 12, 617628 (2000).
[12] G. E. Stavroulakis, Auxetic behaviour: appearance and engineering applications. Physica Status Solidi B, Special Issue on Auxetics and Related Systems, Guest Editor: K. Wojciechowski 2004 (in press).
[13] C. R. Houck, J. F. Joines, and M. G. Kay, A genetic algorithm for function optimization: A Matlab implementation. NCSU-IE TR 95-09 1995.
[14] H. F. Tiersten, Linear Piezoelectric Plate Vibration, Plenum Press New York (1969).
[15] H. S. Tzou, Piezoelectric Shells, Kluwer Academic Publishers The Netherlands (1993).
[16] C. R. Cowper, The shear coefficient in Timoshenko’s beam theory. ASME J. Appl. Mech. 33,
335-340 (1966).
[17] R. S. Lakes, Design considerations for negative Poisson’s ratio materials. J. Mech. Design-T.
ASME 115, 696-700 (1993).
[18] M. Ruzzene, L. Mazzarella, P. Tsopelas, and F. Scarpa, Wave propagation in sandwich plates with periodic auxetic core. Journal of Intelligent Material Systems and Structures 13(9), 587-597 (2002).
[19] M. Ruzzene and F. Scarpa, Control of wave propagation in sandwich beams with auxetic core. Journal of Intelligent Material Systems and Structures, 14(7), 443-453 (2003).
[20] G. Futsitzi, D. Marinova, E. Hadjigeorgiou and G. Stavroulakis, Robust H-2 vibration control of beams with piezoelectric sensors and actuators. Proceedings of Physics and Control Conference St. Petersburg Russia, 20-22.08.2003, Vol. 1, pp. 157-162.
[21] G. Stavroulakis, G. Futsitzi, E. Hadjigeorgiou, D. Marinova, and C. Baniotoloulos, Design of
smart beams for suppresion of wind induced vibrations. The 9th International Conference on Civil and Structural Engineering Computing, Egmond and Zee, The Netherlands 2003, Paper 114,
B.H.V. Topping (Editor), Civil-Comp Press.
This paper presents a study of the implications of using auxetic materials in the design of
smart structures. By using auxetic materials as core and piezoelectric actuators as face layers to provide control forces, the problem of the shape control of sandwich beams is analyzed under loading conditions. The mechanical model is based on the shear deformable theory for beams and the linear theory of piezoelectricity. The numerical solution of the model is based on superconvergent (locking-free) finite elements for the beam theory, using Hamilton’s principle. The optimal voltages of the piezo-actuators for shape control of a cantilever beams with classical and auxetic material are determined by using a genetic optimization procedure. Related numerical solutions of static problems demonstrate the role of auxetic material in the deformation, shape control and stress distribution of the beam and related twodimensional
composite elastic structures.
Key words:
Auxetic materials, finite element analysis, genetic optimization., shape control, smart beams and plates
References:
[1] H. Janocha (Ed.), Adaptronics and Smart Structures, Springer-Verlag Berlin (1999).
[2] P. Gaudenzi, F. Enrico, V. Koumousis, and C. Gantes, Shape control of statically indeterminate lami nated beams with piezoelectric actuators. J. Intell. Mater. Syst. 9, 291-300 (1998).
[3] B. N. Agrawal and K E. Treanor, Shape control of statically indeterminate laminated beams with piezoelectric actuators. Smart Mater. Struct. 8, 729-740 (1999).
[4] C. Chee, L. Tong, and G. Steven, A buildup voltage (BVD) algorithm for shape control of smart plate structures. Engineering Structures 24, 5-11 (2000).
[5] H. Irschik, A review on static and dynamic shape control of structures using piezoelectric
actuation. Computational Mechanics 26, 115-128 (2002).
[6] E. P. Hadjigeorgiou, G. Foutsitzi, and G. E. Stavroulakis, Shape control of beams with piezo
electric actuators Proc. 6th Hellenic-European Conference on Computer Mathematics and its
Applications 25-27 September Athens HERCMA 2003, E. A. Lipitakis (Editor), LEA Publishers,
Vol. I, pp. 164-168 (2003).
[7] Z. Friedman and J. B. Kosmatka, An inproved two-node Timoshenko beam finite element. Comput. Struct. 47 473-481 (1993).
[8] J. N. Reddy, On locking-free shear deformable beam finite elements. Comput. Methods Appl. Mech. Engrg. 149 113-132 (1997).
[9] W. Yang, Z. M. Li, W. Shi, B. H. Xie, and M. B. Yang. On auxetic materials. J. Mater. Sci. 39,
3269-3279 (2004).
[10] T. Matsuoka, S. Yamamoto, and M. Takahara, Prediction of structures and mechanical properties of composites using genetic algorithm andfinite element method. J. Mater. Sci. 36, 27-33 (2001).
[11] K E. Evans and A. Alderson, Auxetic materials: Functional materials and structures from lateral thinking. Adv. Mater. 12, 617628 (2000).
[12] G. E. Stavroulakis, Auxetic behaviour: appearance and engineering applications. Physica Status Solidi B, Special Issue on Auxetics and Related Systems, Guest Editor: K. Wojciechowski 2004 (in press).
[13] C. R. Houck, J. F. Joines, and M. G. Kay, A genetic algorithm for function optimization: A Matlab implementation. NCSU-IE TR 95-09 1995.
[14] H. F. Tiersten, Linear Piezoelectric Plate Vibration, Plenum Press New York (1969).
[15] H. S. Tzou, Piezoelectric Shells, Kluwer Academic Publishers The Netherlands (1993).
[16] C. R. Cowper, The shear coefficient in Timoshenko’s beam theory. ASME J. Appl. Mech. 33,
335-340 (1966).
[17] R. S. Lakes, Design considerations for negative Poisson’s ratio materials. J. Mech. Design-T.
ASME 115, 696-700 (1993).
[18] M. Ruzzene, L. Mazzarella, P. Tsopelas, and F. Scarpa, Wave propagation in sandwich plates with periodic auxetic core. Journal of Intelligent Material Systems and Structures 13(9), 587-597 (2002).
[19] M. Ruzzene and F. Scarpa, Control of wave propagation in sandwich beams with auxetic core. Journal of Intelligent Material Systems and Structures, 14(7), 443-453 (2003).
[20] G. Futsitzi, D. Marinova, E. Hadjigeorgiou and G. Stavroulakis, Robust H-2 vibration control of beams with piezoelectric sensors and actuators. Proceedings of Physics and Control Conference St. Petersburg Russia, 20-22.08.2003, Vol. 1, pp. 157-162.
[21] G. Stavroulakis, G. Futsitzi, E. Hadjigeorgiou, D. Marinova, and C. Baniotoloulos, Design of
smart beams for suppresion of wind induced vibrations. The 9th International Conference on Civil and Structural Engineering Computing, Egmond and Zee, The Netherlands 2003, Paper 114,
B.H.V. Topping (Editor), Civil-Comp Press.
