Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-13T18:19:19.684Z Has data issue: false hasContentIssue false

5 - Plate Modeling with Induced-Strain Actuation

Published online by Cambridge University Press:  18 December 2013

Inderjit Chopra  and
Jayant Sirohi
Inderjit Chopra
Affiliation:
University of Maryland, College Park
Jayant Sirohi
Affiliation:
University of Texas, Austin
Get access

Summary

The previous chapter discussed the modeling of beam-like structures with induced-strain actuation. Many practical structures can be simplified and analyzed as beams, but such an assumption is not accurate in a large number of other structures, such as fuselage panels in aircraft, low aspect-ratio wings, and large control surfaces. It is possible to treat such structures as plates and perform a simple two-dimensional analysis to estimate their behavior. Some of the theories discussed in the previous chapter can be extended to two-dimensional plate-like structures. This chapter describes the modeling of isotropic and composite plate structures with induced-strain actuation. It will combine both the actuators and substrate into one integrated structure to model its behavior. The discussion focuses on induced-strain actuation by means of piezoceramic sheets, but the general techniques may be equally applicable to other forms of induced-strain actuation.

Plate analysis, including induced-strain actuation, is based on the classical laminated plate theory (CLPT), sometimes referred to as classical laminated theory (CLT). It is an equivalent single layer (ESL) plate theory in which the effects of transverse shear strains are neglected. It is valid for thin plates that have thicknesses of one to two orders of magnitude smaller than their planar dimensions (length and width). In the CLPT formulation, a plane-stress state assumption is used.

Classical Laminated Plate Theory (CLPT) Formulation without Actuation

A composite laminate consists of a number of laminae or plies, each with different elastic properties.

Type
Chapter
Information
Smart Structures Theory , pp. 446 - 580
Publisher: Cambridge University Press
Print publication year: 2013

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] J. N., Reddy. A simple higher-order theory for laminated composite plates. Journal of Applied Mechanics, Transactions of ASME, 51(4):745–752,1984.Google Scholar
[2] A., Nosier, R. K., Kapania, and J. N., Reddy. Free vibration analysis of laminated plates using a layerwise theory. AIAA Journal, 31(12):2335–2346, December 1993.Google Scholar
[3] J. N., Reddy. A generalization of two-dimensional theories of laminated composite plates. Communications in Applied Numerical Methods, 3(3):173–180, 1987.Google Scholar
[4] C. T., Sun and J. M., Whitney. Theories for the dynamic response of laminated plates. AIAA Journal, 11(2):178–183, February 1973.Google Scholar
[5] D.H., Robbins and I., Chopra. The effect of laminate kinematic assumptions on the global response of actuated plates. Journal of Intelligent Material Systems and Structures, 17(4): 273–299, 2006.Google Scholar
[6] J. N., Reddy. On the generalization of displacement-based laminate theories. Applied Mechanics Reviews, 42(11):S213–S222, 1989.Google Scholar
[7] A., Chattopadhyay, J., Li, and H., Gu. Coupled thermo-piezoelectric-mechanical model for smart composite laminate. AIAA Journal, 37(12):1633–1638, December 1999.Google Scholar
[8] X., Zhou, A., Chattopadhyay, and H., Gu. Dynamic response of smart composites using a coupled thermo-piezoelectric-mechanical model. AIAA Journal, 38(10):1939–1948, October 2000.Google Scholar
[9] D. H., Robbins and I., Chopra. Quantifying the local kinematic effect in actuated plates via strain-energy distribution. Journal of Intelligent Material Systems and Structures, 18(6):569–589, 2007.Google Scholar
[10] E. F., Crawley and K. B., Lazarus. Induced-strain actuation of isotropic and anisotropic plates. AIAA Journal, 29(6):944–951, June 1991.Google Scholar
[11] C. K., Lee. In piezoelectric laminates: Theory and experiments for distributed sensors and actuators, pages 75–168. Intelligent Structural Systems, edited by H.S., TzouandG. L., Anderson, Kluwer Academic Publishers, 1992.Google Scholar
[12] C. K., Lee. Theory of laminated piezoelectric plates for the design of distributed sensors/actuators: Part I: Governing equations and reciprocal relationships. Journal of the Acoustical Society of America, 87(3):1144–1158, 1990.Google Scholar
[13] B. T., Wang and C. A., Rogers. Laminate plate theory for spatially distributed induced-strain actuators. Journal of Composite Materials, 25(4):433–452, April 1991.Google Scholar
[14] C. C., Lin, C. Y., Hsu, and H. N., Huang. Finite element analysis on deflection control of plates with piezoelectric actuators. Composite Structures, 35(4):423–133,1996.Google Scholar
[15] C. H., Hong and I., Chopra. Modeling and validation of induced-strain actuation of composite coupled plates. AIAA Journal, 37(3):372–377, March 1999.Google Scholar
[16] P., Heyliger. Exact solutions for simply-supported laminated piezoelectric plates. Journal of Applied Mechanics, 64(2):299–306, 1997.Google Scholar
[17] E., Carrera. An improved Reissner-Mindlin type model for the electromechanical analysis of multi-layered plates including piezo-layers. Journal of Intelligent Material Systems and Structures, 8(3):232–248, March 1997.Google Scholar
[18] J. A., Mitchell and J. N., Reddy. A refined hybrid plate theory for composite laminates of piezoelectric laminae. International Journal of Solids and Structures, 32(16):2345–2367, August 1995.Google Scholar
[19] D. H., Robbins and J. N., Reddy. An efficient computational model for the stress analysis of smart plate structures. Smart Materials and Structures, 5(3):353–360, 1996.Google Scholar
[20] R. C., Batra and S., Vidoli. Higher-order piezoelectric plate theory derived from a three-dimensional variational principle. AIAA Journal, 40(1):91–104, January 2002.Google Scholar
[21] S. K., Ha, C., Keilers, and F. K., Chang. Finite element analysis of composite structures containing distributed piezoelectric sensors and actuators. AIAA Journal, 30(3):772–780, March 1992.Google Scholar
[22] S. V., Gopinathan, V. V., Varadan, and V. K., Varadan. A review and critique of theories for piezoelectric laminates. Smart Materials and Structures, 9(1):24–18, February 2000.Google Scholar
[23] Y. Y., Yu. Some recent advances in linear and nonlinear dynamical modeling of elastic and piezoelectric plates. Journal of Intelligent Material Systems and Structures, 6(2): 237–254, March 1995.Google Scholar
[24] P., Bisegna and G., Carusa. Mindlin-type finite elements for piezoelectric sandwich plates. Journal of Intelligent Material Systems and Structures, 11(1):14–25, January 2000.Google Scholar
[25] P., Bisegna and F., Maceri. A consistent theory of thin piezoelectric plates. Journal of Intelligent Material Systems and Structures, 7(4):372–389, July 1996.Google Scholar
[26] S., Kapuria and G. G. S., Achary. Electromechanically coupled zigzag third-order theory for thermally loaded hybrid piezoelectric plates. AIAAJournal, 44(1):160–170, 2006.Google Scholar
[27] W., Yu and D. H., Hodges. A simple thermopiezoelastic model for smart composite plates with accurate stress recovery. Smart Materials and Structures, 13(4):926–938, August 2004.Google Scholar
[28] L., Edery-Azulay and H., Abramovich. A reliable plain solution for rectangular plates with piezoceramic patches. Journal of Intelligent Material Systems and Structures, 18(5): 419–433, May 2007.Google Scholar
[29] D. H., Robbins and J. N., Reddy. Modelling of thick composites using a layerwise laminate theory. International Journal for Numerical Methods in Engineering, 36(4):655–677,1993.Google Scholar
[30] P., Heyliger, G., Ramirez, and D. A., Saravanos. Coupled discrete-layer finite elements for laminated piezoelectric plates. Communications in Numerical Methods in Engineering, 10(12):971–981, 1994.Google Scholar
[31] D. A., Saravanos, P. R., Heyliger, and D. A., Hopkins. Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates. International Journal of Solids and Structures, 34(3):359–378, 1997.Google Scholar
[32] S. S., Vel and R. C., Batra. Three-dimensional analytical solution for hybrid multilayered piezoelectric plates. Journal of Applied Mechanics, Transactions of the ASME, 67(3): 558–567, September 2000.Google Scholar
[33] J. S., Yang and R. C., Batra. Mixed variational principles in nonlinear piezoelectricity. International Journal of Nonlinear Mechanics, 30(5):719–726, 1995.Google Scholar
[34] S. A., Kulkarni and K. M., Bajoria. Large deformation analysis of piezolaminated smart structures using higher-order shear-deformation theory. Smart Materials and Structures, 16(5):1506–1516, 2007.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×