Abstract
This paper presents the accurate prediction of static behavior of composite beams with arbitrary cross-sections. The asymptotic recursive formulation is reviewed first, where the initial three-dimensional problems are split into the macroscopic 1D problems and the microscopic 2D problems. The finite element formulation for the microscopic 2D problems is then presented in order to find the crosssectional warping solutions. The warping solutions obtained contribute the cross-sectional properties to the macroscopic 1D problems. The end effect of the 1D beam problem is also considered via the kinematic correction for a displacement prescribed boundary. The approach presented is applied to the beams with relatively complicated material distributions and cross-sectional geometry. As numerical test-beds, a three-layered sandwich beam and a composite beam with the multi-cell cross-section are taken to analyze the local deformation. A parametric study is also carried out to investigate the significance of shear deformation due to the cross-sectional orthotropic characteristics. The cross-sectional deformation is predicted based on the asymptotic framework. The accuracy of the present approach is assessed by comparing the results obtained with the 3D FEM solutions obtained by ANSYS.
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References
J.-S. Kim and K. W. Wang, Vibration analysis of composite beams with end effects via the formal asymptotic method, ASME: Journal of Vibration and Acoustics, 132 (2010) 041003:1–8.
V. L. Berdichevsky, On the energy of an elastic rod, Journal of Applied Mathematics and Mechanics (PMM), 45(4) (1981) 518–529.
C. E. S. Cesnik, V. G. Sutyrin and D. H. Hodges, Refined theory of composite beams: the role of short-wavelength extrapolation, International Journal of Solids and Structures, 33(10) (1996) 1387–1408.
C. E. S. Cesnik, V. G. Sutyrin and D. H. Hodges, VABS: a new concept for composite rotor blade cross-sectional modeling, Journal of American Helicopter Society, 42(1) (1997) 27–38.
B. Popescu and D. H. Hodges, On asymptotically correct Timoshenko-like anisotropic beam theory, International Journal of Solids and Structures, 37 (2000) 535–558.
W. Yu, D. H. Hodges, V. V. Volovoi and C. E. S. Cesnik, On Timoshenko-like modeling of initially curved and twisted composite beams, International Journal of Solids and Structures 39 (2002) 5101–5121.
L. Trabucho and J. M. Viano, Mathematical modeling of rods. In: Ciarlet PG, Lions JL. Handbook of Numerical Analysis, North-Holland (1996) Vol. 4.
R. D. Gregory and F. Y. M. Wan, Decaying states of plane strain in a semi-infinite strip and boundary conditions for plate theory, Journal of Elasticity, 14 (1984) 27–64.
N. Buannic and P. Cartraud, Higher-order effective modeling of periodic heterogeneous beams. I. Asymptotic expansion method, International Journal of Solids and Structures, 38 (2001a) 7139–7161.
N. Buannic, P. Cartraud, Higher-order effective modeling of periodic heterogeneous beams. II. Derivation of the proper boundary conditions for the interior asymptotic solution, International Journal of Solids and Structures, 38 (2001b) 7168–7180.
H. Fan and G. E. O. Widera, On the proper boundary conditions for a beam, Journal of Applied Mechanics, 59 (1992) 915–922.
H. Fan and G. E. O. Widera, On use of variational principles to derive beam boundary conditions, Journal of Applied Mechanics, 61 (1992) 470–471.
C. O. Horgan and J. G. Simmonds, Asymptotoic analysis of an end-loaded transversely isotropic, elastic, semi-infinite strip weak in shear, International Journal of Solids and Structures, 27 (1991) 1895–1914.
J. M. Duva and J. G. Simmonds, The usefulness of elementary theory for the linear vibrations of layered, orthotropic elastic beams and corrections due to two-dimensional end effect, Journal of Applied Mechanics, 58 (1991) 175–180.
J.-S. Kim, M. Cho and E. C. Edward, An asymptotic analysis of composite beams with kinematically corrected end effects, International Journal of Solids and Structures, 45 (2008) 1954–1977.
M. Peters and K. Hackl, Numerical aspects of the eXtended finite element method, Proceeding in Applied Mathematics and Mechanics, 5 (2005), 355–356.
R. L. Taylor, P. J. Beresford and E. L. Wilson, A nonconforming element for stress analysis, International Journal for Numerical Methods in Engineering, 10 (1976) 1211–1219.
ANSYS, ANSYS user’s guide release 9.0, 2004.
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This paper was recommended for publication in revised form by Editor Keum Shik Hong
Joonho Jeong received the B.S. degree from Chungang University, Korea in 2005, and the M.S. degree from Seoul National University, Korea in 2007. He is currently Ph.D candidate in Seoul National University, Korea. His research interests include solid mechanics, structural vibration and multiscale mechanics.
Jun-Sik Kim received the B.S. and M.S. degrees from Inha University, Korea in 1994 and 1996, respectively, and the Ph.D. degree from the Pennsylvania State University, USA in 2005, all in aerospace engineering. In 2009, he joined Kumoh National Institute of Technology, Korea, where he is currently an assistant professor in the department of intelligent mechanical engineering. His research interests include solid mechanics, smart structures, helicopter dynamics, and numerical methods.
Yeon June Kang received his B.S. and M.S. degrees in Mechanical Design and Production Engineering from Seoul National University in 1988 and 1990, respectively. He then went on to receive a Ph.D. degree in Acoustics and Vibration from School of Mechanical Engineering, Purdue University in 1994. After his Ph.D., he continued to work as a Postdoctoral Research until 1996. Since 1997, Dr. Kang is working at the Department of Mechanical and Aerospace Engineering, Seoul National University. Dr. Kang’s research interests are in the area of acoustical materials, noise and vibration in automotive engineering and Korean Bells.
Maenghyo Cho received the B.S. and M.S. degree from Seoul National University, Korea in 1984 and 1986, respectively, and Ph.D degree from University of Washington, Seattle, USA in 1993. In 1999, he joined Seoul National University, where he is currently a professor in school of Mechanical and Aerospace Engineering. His research interests include multiscale mechanics, Molecular dynamics, Solid/Structural Mechanics, and Computational Mechanics.
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Jeong, J., Kim, JS., Kang, Y.J. et al. A cross-sectional analysis of composite beams based on asymptotic framework. J Mech Sci Technol 26, 161–172 (2012). https://doi.org/10.1007/s12206-011-1022-7
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DOI: https://doi.org/10.1007/s12206-011-1022-7