An asymptotically correct analysis of passive anisotropic thin-walled open cross-section beam-like structures using the variational asymptotic method (VAM) is extended to include embedded macro fiber composites. Application of the VAM to beam-like structures splits the problem into non-linear 1D theory along the selected beam reference line and linear 2D generalized 5 × 5 Vlasov theory augmented by a 5 × 1 actuation vector over the cross-section. The linear 2D cross-sectional theory is validated against the University of Michigan/variational beam sectional analysis 2D finite element software. The validation examples selected were based on practical cross-sectional geometry and material anisotropy under DC actuation voltage. Actuation-induced deformations predicted at the beam reference line are obtained using an intrinsic geometrically exact beam theory for open cross-sections. The predicted generalized deformations are compared with those obtained using the 3D finite element analysis software ANSYS Multiphysics, which further validates the extended theory. The analytical theory is shown to be straightforward to implement and efficient, yet sufficiently reliable to perform interdisciplinary studies and optimization of various engineering applications of such structures.
Badir, A.M.1992. ‘‘Analysis of Advanced Thin-walled Composite Structures,’’ PhD Thesis, Georgia Institute of Technology.
3.
Berdichevsky, V.L.1982. ‘‘On the Energy of an Elastic Rod, ’’ PMM, 45:518-529.
4.
Berdichevsky, V., Armanios, E. and Badir, A.1992. ‘‘Theory of Anisotropic Thin-walled Closed-crosssection Beams,’’ Composites Engineering, 2:411-432.
5.
Cesnik, C.E.S. and Hodges, D.H.1997. ‘‘VABS: A New Concept for Composite Rotor Blade Cross-sectional Modeling,’’ Journal of the American Helicopter Society, 42(1):27-38.
6.
Cesnik, C.E.S., Last, H.R. and Martin, C.A.2004. ‘‘A Framework for Morphing Capability Assessment,’’ In: Proceedings of the 45th AIAA/ASME/ASCHE/ASC Structures, Structural Dynamics and Materials Conference, Palm Springs, CA, 19-22 April, AIAA, pp. 1582-1592.
7.
Cesnik, C.E.S. and Ortega-Morales, M.2001. ‘‘Active Beam Cross-sectional Modeling, ’’ Journal of Intelligent Material Systems and Structures, 12(7):483-496.
8.
Cesnik, C.E.S. and Palacios, R.2003. ‘‘Modeling Piezocomposite Actuators Embedded in Slender Structures,’’ In: Proceedings of the 44th AIAA/ASME/ASCHE/AHS Structures, Structural Dynamics and Materials Conference, Norfolk, Virginia, 7-10 April.
9.
Cesnik, C.E.S. and Shin, S.2001. ‘‘On the Modeling of Integrally Actuated Helicopter Blades,’’ International Journal of Solids and Structures, 38:1765-1789.
10.
Cesnik, C.E.S., Sutyrin, V.G. and Hodges, D.H.1993. ‘‘A Refined Composite Beam Theory Based on the Variational-asymptotic Method,’’ In: Proceedings of the 34th Structures, Structural Dynamics, and Materials Conference , La Jolla, California, April, AIAA, number 93-1616, pp. 2710-2720.
11.
Derham, R., Weems, D., Mathew, M.B. and Bussom, R.2001. ‘‘The Design Evolution of an Active Materials Rotor,’’ In: AHS 57th Annual Forum, The Vertical Flight Society, The American Helicopter Society , 9-11 May, Washington, DC.
12.
Gjelsvik, A.1981. The Theory of Thin Walled Bars, 1stedn, John Wiley & Sons, New York .
13.
Griffiths, J., Khouli, F. and Afagh, F.F.2009. ‘‘Nonlinear Static Analysis of Reducible Thin-wall Active Open Cross-section Beams Based on Generalized Vlasov Theory,’’ In: The Third International Conference on Integrity, Reliability and Failure (IRF’2009), Porto, Portugal.
14.
Hodges, D.H.1990. ‘‘A Mixed Variational Formulation Based on Exact Intrinsic Equations for Dynamics of Moving Beams,’’ Internataional Journal of Solids and Structures, 26(11):1253-1273.
15.
Hodges, D.H. and Volovoi, V.V.2000. ‘‘Theory of Anisotropic Thin-walled Beams ,’’ Journal of Applied Mechanics, 67:453-459.
16.
Jha, A.K. and Kudva, J.N.2004. ‘‘Morphing Aircraft Concepts, Classifications, and Challenges,’’ In: Proceedings of the SPIE, Smart Structures and Materials 2004. Industrial and Commercial Applications of Smart Structures Technologies, San Diego, CA, Vol. 5388, pp. 213-224.
17.
Khouli, F.2009. ‘‘Modelling and Attenuation Feasibility of the Aeroelastic Response of Active Helicopter Rotor Systems During the Engagement/Disengagement Phase of Maritime Operation,’’ PhD Thesis, Carleton University, Department of Mechanical and Aerospace Engineering.
18.
Khouli, F., Afagh, F.F. and Langlois, R.G.2006. ‘‘Actuation of Slender Thin-wall Anisotropic Open Cross-section Beams Based on Asymptotically-correct Vlasov Theory,’’ In: Proceedings of the 17th International Conference of Adaptive Structures and Technologies, Taipei, Taiwan, 16-19 October.
19.
Khouli, F., Langlois, R.G. and Afagh, F.F.2007. ‘‘Analysis of Active Closed-cross Section Slender Beams Based on Asymptotically-correct Thin-wall Beam Theory, ’’ Smart Materials and Structures, 16(1):221-229.
20.
Mistry, M., Gandhi, F. and Chandra, R.2008. ‘‘Twist Control of an I-beam Through Vlasov Bimoment Actuation,’’ In: Proceedings of the 49th AIAA/ASME/ASCHE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Schaumburg, IL, April, AIAA.
21.
Rodgers, J.P.1999. ‘‘Development of an Integral Twist-actuated Rotor Blade for Individual Blade Control,’’ PhD Thesis, Massachusetts Institute of Technology (MIT).
22.
Roy, S., Yu, W. and Han, D.2007. ‘‘An Asymptotically Correct Classical Model for Smart Beams,’’ International Journal of Solids and Structures, 44(25-26):8424-8439.
23.
Standards Committee of the IEEE Ultrasonics Ferroelectrics and Frequency Control Society.1992. IEEE Standard on Piezoelectricity-ANSI/IEEE Standard 176-1987, The American Institute of Physics.
24.
The International Center for Numerical Methods in Engineering.2009. GiD The Personal Pre and Post Processor , International Center for Numerical Methods in Engineering , Barcelona.
25.
Volovoi, V.V. and Hodges, D.H.2002. ‘‘Single- and Multi-celled Composite Thin-walled Beams,’’ AIAA Journal, 40(5):960-965.
26.
Volovoi, V.V., Hodges, D.H., Berdichevsky, V.L. and Sutyrin, V.G.1999. ‘‘Asymptotic Theory for Static Behavior of Elastic Anisotropic I-beams,’’ International Journal of Solids and Structures, 36:1017-1043.
27.
Volovoi, V.V., Hodges, D.H., Cesnik, C.E.S. and Popescu, B.2001. ‘‘Assessment of Beam Modeling Methods for Rotor Blade Application,’’ Mathematical and Computer Modelling, 33:1099-1112.
28.
Yu, W.2009. VABS Manual, Utah State University .
29.
Yu, W. and Hodges, D.H.2004. ‘‘Elasticity Solutions Versus Asymptotic Sectional Analysis of Homogeneous, Isotropic, Prismatic Beams,’’ Journal of Applied Mechanics, 71(1):15-23.
30.
Yu, W., Volovoi, V.V., Hodges, D.H. and Hong, X.2002. ‘‘Validation of the Variational Asymptotic Beam Sectional Analysis (VABS),’’ AIAA Journal , 40(10):2105-2113.
31.
Yu, W.1., Hodges, D.H., Volovoi, V.V. and Fuchs, E.D.2005. ‘‘A Generalized Vlasov Theory for Composite Beams,’’ Thin-Walled Structures, 43(9):1493-1511.
