Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T05:55:44.846Z Has data issue: false hasContentIssue false
  • English
  • Français

A Finite Element Model for Composite Beams with Piezoelectric Layers using A Sinus Model

Published online by Cambridge University Press:  05 May 2011

S. B. Beheshti-Aval  and
M. Lezgy-Nazargah
S. B. Beheshti-Aval*
Affiliation:
Department of Civil Engineering, Khajeh Nasir Toosi University of Technology (KNTU), Tehran, Iran
M. Lezgy-Nazargah*
Affiliation:
Department of Civil Engineering, Khajeh Nasir Toosi University of Technology (KNTU), Tehran, Iran
*
* Assistant Professor, corresponding author
** Ph.D. student
Get access

Abstract

In this study, finite element modeling of composite beams with distributed piezoelectric sensors and actuators which is based upon a coupled electromechanical model has been considered. For modeling of mechanical displacement through the thickness, a sinus model that satisfies continuity conditions of transverse shear stresses and the boundary conditions on the upper and lower surfaces of the beam has been employed. In the presented model, the number of unknowns is not dependent on the number of layers. The variation of electric potential in each piezoelectric layer has been modeled using layer-wise theory. By applying the virtual work principle (VWP), a formulation has been developed for a twonodded Hermitian-2(n + 1) layer-wise nodded element for a n-layered beam. The VWP leads to a derivation that could include dynamic analysis. However, in this study only static problems have been considered. Comparison of results obtained from this formulation with available works in the literature, demonstrates efficiency of proposed model in analysis of laminated beams under mechanical and electrical loadings.

Keywords

Finite elementComposite beamsPiezoelectric layersSinus modelTransverse stress.
Type
Articles
Information
Journal of Mechanics , Volume 26 , Issue 3 , September 2010 , pp. 335 - 344
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Crawley, E. F. and Luis, J., “Use of Piezoelectric Actuators as Element of Intelligent Structures,” American Institute of Aeronautics and Astronautics, 25, pp. 1373–1385 (1987).CrossRefGoogle Scholar
2.Tzou, H. S. and Grade, M., “Theoretical Analysis of a Multi-Layered Thin Shell Coupled with Piezoelectric Shell Actuators for Distributed Vibration Controls,” Journal of Sound and Vibration, 132, pp. 433–450 (1989).CrossRefGoogle Scholar
3.Wang, B. T. and Rogers, C. A., “Laminate Plate Theory for Spatially Distributed Induced Strain Actuators,” Journal of Composite Material, 25, pp. 433–425 (1991).CrossRefGoogle Scholar
4.Sung, C. K., Chen, T. F. and Chen, S. G., “Piezoelectric Modal Sensor/Actuator Design for Monitoring /Generating Flexural and Torsional Vibrations of Cylindrical Shells,” Journal of Sound and Vibration, 118, pp. 48–55 (1996).Google Scholar
5.Wu, C. P., Syu, Y. S. and Lo, J. Y., “Three-Dimensional Solutions for Multilayered Piezoelectric Hollow Cylinders by an Asymptotic Approach,” International Journal of Mechanical Sciences, 49, pp. 669–689 (2007).CrossRefGoogle Scholar
6.Wu, C. P. and Liu, K. Y., “A State Space Approach for the Analysis of Doubly Curved Functionally Graded Elastic and Piezoelectric Shells,” CMC: Computers, Materials and Continua, 6, pp. 144–199 (2007).Google Scholar
7.Wu, C. P., Chm, K. H. and Wang, Y. M., “A Review on the Three-Dimensional Analytical Approaches of Multilayered and Functionally Graded Piezoelectric Plates and Shells,” CMC: Computers, Materials and Continua, 18, pp. 93–132 (2008).Google Scholar
8.Allik, H. and Hughes, T. J. R., “Finite Element Method for Piezoelectric Vibration,” International Journal for Numerical Methods in Engineering, 2, pp. 151–157 (1970).CrossRefGoogle Scholar
9.Tzou, T. S. and Tseng, C. I., “Distributed Piezoelectric Sensor/Actuator Design for Dynamic Measurement/Control of Distributed Parameter System: A Piezoelectric Finite Element Approach,” Journal of Sound and Vibration, 138, pp. 17–34 (1990).CrossRefGoogle Scholar
10.Xu, K. M., Noor, A. K. and Tang, Y.,“Three-Dimensional Solutions for Coupled Thermo-Electro-Elastic Response of Multi-Layered Plates,” Computer Methods in Applied Mechanics and Engineering, 126, pp. 355–371 (1995).CrossRefGoogle Scholar
11.Semedo Garcao, J. E., Mota Soares, C. M., Mota Soares, C. A. and Reddy, J. N., “Analysis of Laminated Adaptive Plate Structures Using Layer-Wise Finite Element Models,” Composite Structures, 82, pp. 1939–1959 (2004).CrossRefGoogle Scholar
12.Garcia Lage, R., Mota Soares, C. M., Mota Soares, C. A. and Reddy, J. N., “Analysis of Laminated Adaptive Plate Structures by Mixed Layer-Wise Finite Element Models,” Composite Structures, 66, pp. 269–276 (2004).CrossRefGoogle Scholar
13.Garcia Lage, R., Mota Soares, C. M., Mota Soares, C. A. and Reddy, J. N., “Modeling of Piezolaminated Plates Using Layer-Wise Mixed Finite Element Models,” Composite Structures, 82, pp. 1849–1863 (2004).CrossRefGoogle Scholar
14.Heyliger, P. R. and Saravanos, D. A., “Coupled Discrete-Layer Finite Elements for Laminated Piezoelectric Plates,” Communications in Numerical Methods in Engineering, 10, pp. 971–981 (1994).CrossRefGoogle Scholar
15.Saravanos, D. A., Heyliger, P. R. and Hopkins, D. A., “Layer-Wise Mechanics and Finite Element Model for the Dynamic Analysis of Piezoelectric Composite Plates,” International Journal of Solids and Structures, 34, pp. 359–378(1997).CrossRefGoogle Scholar
16.Mitchell, J. A. and Reddy, J. N., “A Refined Plate Theory for Composite Laminates with Piezoelectric Laminate,” International Journal of Solids and Structures, 32, pp. 2345–2367(1995).CrossRefGoogle Scholar
17.Sheikh, A. H., Topdar, P. and Haider, S., “An Appropriate FE Model for Through Thickness Variation of Displacement and Potential in Thin/Moderately Thick Smart Laminates,” Composite Structures, 51, pp. 401–409 (2001).CrossRefGoogle Scholar
18.Carrera, E., “Theories and Finite Elements for Multilayered, Anisotropic, Composite Plates and Shells,” Archives of Computational Methods in Engineering, 9, pp. 87–140 (2002).CrossRefGoogle Scholar
19.Noor, A. K. and Burton, W. S., “Assessment of Shear Deformation Theories for Multilayered Composite Plates,” Applied Mechanics Reviews, 42, pp. 1–13 (1989).CrossRefGoogle Scholar
20.Reddy, J. N. and Robbins, D H., “Theories and Computational Models for Composite Laminates,” Applied Mechanics Reviews, 1, pp. 147–169 (1994).CrossRefGoogle Scholar
21.Di Sciuva, M., “A Refined Transverse Shear Deformation Theory for Multilayered Anisotropic Plates,” Atti Accademia Scienze Torino, 118, pp. 279–295 (1984).Google Scholar
22.Lue, D. and Li, X., “An Overall View of Laminate Theories Based on Displacement Hypothesis,” Journal of Composite Materials, 30, pp. 1539–1560(1996).Google Scholar
23.Bhaskar, K. and Varadan, T. K., “Refinement of Higher Order Laminated Plate Theories,” American Institute of Aeronautics and Astronautics, 27, pp. 1830–1831 (1989).CrossRefGoogle Scholar
24.Di Sciuva, M., “Multilayered Anisotropic Plate Models with Continuous Interlaminar Stress,” Computers and Structures, 22, pp. 149–167 (1992).CrossRefGoogle Scholar
25.Lee, C. Y. and Liu, D., “Interlaminar Shear Stress Continuity Theory for Laminated Composite Plates,” American Institute of Aeronautics and Astronautics, 29, pp. 2010–2012(1991).CrossRefGoogle Scholar
26.Cho, M. and Parmerter, R. R., “Efficient Higher Order Plate Theory for General Lamination Configurations,” American Institute of Aeronautics and Astronautics, 31, pp. 1299–1308(1993).CrossRefGoogle Scholar
27.Reddy, J. N., “A Simple Higher-Order Theory for Laminated Composites,” Journal of Applied Mechanics-Transactions of the ASME, 51, pp. 745–752 (1984).CrossRefGoogle Scholar
28.Chee, C. Y. K., Tong, L. and Steven, P. G., “A Mixed Model for Composite Beams with Piezoelectric Actuators and Sensors,” Smart Materials and Structures, 8, pp. 417–432 (1999).CrossRefGoogle Scholar
29.Vidal, P. and Polit, O., “A Family of Sinus Finite Elements for the Analysis of Rectangular Laminated Beams,” Composite Structures, 84, pp. 56–72 (2008).CrossRefGoogle Scholar
30.Benjeddou, A., “Advances in Piezoelectric Finite Element Modeling of Adaptive Structural Elements: A Survey,” Computers and Structures, 76, pp. 347–363 (2000).CrossRefGoogle Scholar
31.Cho, M. and Oh, J., “Higher Order Zig-Zag Plate Theory Under Thermo-Electric-Mechanical Loads Combined,” Composites Part B: Engineering, 34, pp. 67–82 (2003).CrossRefGoogle Scholar
32.Cho, M. and Oh, J., “Higher Order Zig-Zag Theory for Fully Coupled Thermo-Electric-Mechanical Smart Composite Plates,” International Journal of Solids and Structures, 41, pp. 1331–1356 (2004).CrossRefGoogle Scholar
33.Oh, J. and Cho, M., “A Finite Element Based on Cubic Zig-Zag Plate Theory for the Prediction of Thermo-Electric-Mechanical Behaviors,” International Journal of Solids and Structures, 41, pp. 1357–1375 (2004).CrossRefGoogle Scholar
34.Topdar, P., Chakraborti, A. and Sheikh, A. H., “An Efficient Hybrid Plate Model for Analysis and Control of Smart Sandwich Laminates,” Computer Methods in Applied Mechanics and Engineering, 193, pp. 4591–4610 (2004).CrossRefGoogle Scholar
35.Saravanos, D. A. and Heyliger, P. R., “Coupled Layer-Wise Analysis of Composite Beams with Embedded Piezoelectric Sensors and Actuators,” Journal of Intelligent Material Systems and Structures, 6, pp. 350–363 (1995).CrossRefGoogle Scholar
36.Hwang, W. S. and Park, H. C, “Finite Element Modeling of Piezoelectric Sensors and Actuators,” American Institute of Aeronautics and Astronautics, 31, pp.930–937 (1993).CrossRefGoogle Scholar
37.Tzou, H. S. and Ye, R, “Analysis of Piezoelastic Modeling of Adaptive Composite Structures Using a Structures with Laminated Piezoelectric Structures with Laminated Piezoelectric Triangle Shell Elements,” American Institute of Aeronautics and As-tronautics, 34, pp. 110–115 (1996).CrossRefGoogle Scholar
38.Suleman, A. and Venkaya, V. B., “A Simple Finite Element Formulation for a Laminated Composite Plate with Piezoelectric Layers,” Journal of Intelligent Material Systems and Structures, 6, pp. 776–782 (1995).CrossRefGoogle Scholar
39.Correia, F. V. M., Gomes, M. A. A. and Suleman, A., “Modeling and Design of Adaptive Composite Structures,” Computer Methods in Applied Mechanics and Engmeenng, 185, pp. 325–346 (2000).CrossRefGoogle Scholar
40.Fukunaga, H., Hu, N. and Ren, G. X., “Finite Element Modeling of Adaptive Composite Structures Using a Reduced Higher-Order Plate Theory Via Penalty Functions,” International Journal of Solids and Structures,38, PP. 8735–8752 (2001).CrossRefGoogle Scholar