Modeling of Interactive Buckling in Sandwich Struts with Functionally Graded Cores
Publication: Journal of Engineering Mechanics
Volume 139, Issue 8
Abstract
An analytical pilot model for interactive buckling in sandwich struts with cores made from a functionally graded material based on total potential energy principles is presented. Using a Timoshenko beam approach, a system of nonlinear differential and integral equations is derived that predicts critical and secondary instabilities. These are validated against numerical simulations performed within the commercial finite-element package Abaqus. Good agreement is found, and this offers encouragement for more elaborate models to be devised that can account for face-core delamination—a feature where functionally graded materials are known to offer distinct advantages.
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References
Abali, B. E., Völlmecke, C., Woodward, B., Kashtalyan, M., Guz, I., and Müller, W. H. (2012). “Numerical modeling of functionally graded materials using a variational formulation.” Continuum Mech. Thermodyn., 24(4–6), 377–390.
Abaqus 6.6 [Computer software]. Pawtucket, RI, Hibbitt, Karlsson, & Sorensen.
Anderson, T. A. (2003). “A 3-d elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere.” Compos. Struct., 60(3), 265–274.
Apetre, N. A., Sankar, A. V., and Ambur, D. R. (2008). “Analytical modeling of sandwich beams with a functionally graded core.” J. Sandwich Struct. Mater., 10(1), 53–74.
Atanackovic, T. M. (1997). Stability theory of elastic rods, World Scientific, Singapore.
Auto 07p [Computer software]. Montréal, Concordia Univ.
Ávila, A. F. (2007). “Failure mode investigation of sandwich beams with functionally graded core.” Compos. Struct., 81(3), 323–330.
Beghini, A., Bažant, Z. P., Waas, A. M., and Basu, S. (2006). “Postcritical imperfection sensitivity of sandwich or homogenized orthotropic columns soft in shear and in transverse deformation.” Int. J. Solids Struct., 43(9), 5501–5524.
Belytschko, T., Liu, W. K., and Moran, B. (2000). Nonlinear finite elements for continua and structures, Wiley, Chichester, U.K.
Brischetto, S. (2009). “Classical and mixed advanced models for sandwich plates embedding functionally graded cores.” J. Mech. Mater. Struct., 4(1), 13–33.
Carrera, S., Brichetto, S., and Robaldo, A. (2008). “Variable kinematic model for the analysis of functionally graded material plates.” AIAA J., 46(1), 194–203.
Cho, K. N., Bert, C. W., and Striz, A. G. (1991). “Free vibrations of laminated rectangular plates analyzed by higher order individual-layer theory.” J. Sound Vibrat., 145(3), 429–442.
Doedel, E. J., and Oldeman, B. E. (2007). “Continuation and bifurcation software for ordinary differential equations.” Technical Rep. AUTO-07p, Dept. of Computer Science, Concordia Univ., Montréal.
Feldman, E., and Abudi, J. (1997). “Buckling analysis of functionally graded plates subjected to uniaxial loading.” Compos. Struct., 38(1–4), 29–36.
Fox, C. (1987). An introduction to the calculus of variations, Dover, NY.
Frostig, Y., Baruch, M., Vilnay, O., and Sheinman, I. (1992). “A high order theory for the bending of sandwich beams with flexible core.” J. Eng. Mech., 118(5), 1026–1043.
Hibbitt, Karlsson, & Sorensen. (2006). Abaqus/standard: User's manual version 6.6. Hibbitt, Karlsson, & Sorensen, Pawtucket, RI.
Huang, H. Y., and Kardomateas, G. A. (2002). “Buckling and initial post-buckling behavior of sandwich beams including transverse shear.” AIAA J., 40(11), 2331–2335.
Hunt, G. W., and Wadee, M. A. (1998). “Localization and mode interaction in sandwich structures.” Proc. R. Soc. London, Ser. A, 454(1972), 1197–1216.
Javaheri, R., and Eslami, M. R. (2002). “Thermal buckling of functionally graded plates.” AIAA J., 40(1), 162–169.
Ke, L. L., Yang, J., and Kitipornchai, S. (2009). “Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening.” Compos. Struct., 90(2), 152–160.
Léotoing, L., Drapier, S., and Vautrin, A. (2002). “Nonlinear interaction of geometrical and material properties in sandwich beam instabilities.” Int. J. Solids Struct., 39(13–14), 3717–3739.
Li, C., and Weng, G. J. (2002). “Antiplane crack problem in functionally graded piezoelectric materials.” Trans. ASME J. Appl. Mech., 69(4), 481–488.
Logg, A., Mardal, K.-A., and Wells, G. N. (2011). Automated solution of differential equations by the finite element method, Berlin, Springer.
Østergaard, R. C. (2008). “Buckling driven debonding in sandwich columns.” Int. J. Solids Struct., 45(5), 1264–1282.
Park, J. S., and Kim, J. H. (2006). “Thermal postbuckling and vibration analyses of functionally graded plates.” J. Sound Vibrat., 289(1–2), 77–93.
Reddy, J. N. (1984). “A simple higher order theory for laminated composite plates.” J. Appl. Mech., 51(4), 745–752.
Reissner, E. (1945). “The effects of transverse shear deformation on the bending of elastic plates.” J. Appl. Mech., 67, 69–77.
Samsam Shariat, B. A., and Eslami, M. R. (2007). “Buckling of thick functionally graded plates under mechanical and thermal loads.” Compos. Struct., 78(3), 433–439.
Samsam Shariat, B. A., Javaheri, R., and Eslami, M. R. (2005). “Buckling of imperfect functionally graded plates under in-plane compressive loading.” Thin-Walled Struct., 43(7), 1020–1036.
Shen, H. S., and Li, S. R. (2008). “Postbuckling of sandwich plates with FGM face sheets and temperature-dependent properties.” Composites Part B, 39(2), 332–344.
Venkataraman, S., and Sankar, B. V. (2003). “Elasticity solution for stresses in a sandwich beam with functionally graded core.” AIAA J., 41(12), 2501–2505.
Wadee, M. A. (2000). “Effects of periodic and localized imperfections on struts on nonlinear foundations and compression sandwich panels.” Int. J. Solids Struct., 37(8), 1191–1209.
Wadee, M. A. (2002). “Localized buckling in sandwich struts with pre-existing delaminations and geometrical imperfections.” J. Mech. Phys. Solids, 50(8), 1767–1787.
Wadee, M. A., and Blackmore, A. (2001). “Delamination from localized instabilities in compression sandwich panels.” J. Mech. Phys. Solids, 49(6), 1281–1299.
Wadee, M. A., and Hunt, G. W. (1998). “Interactively induced localized buckling in sandwich structures with core orthotropy.” J. Appl. Mech., 65(2), 523–528.
Wadee, M. A., Yiatros, S., and Theofanous, M. (2010). “Comparative studies of localized buckling in sandwich struts with different core bending models.” Int. J. Non-linear Mech., 45(2), 111–120.
Yang, J., Liew, K. M., and Kitipornchai, S. (2006). “Imperfection sensitivity of the post-buckling behavior of high order shear deformable functionally graded plates.” Int. J. Solids Struct., 43(17), 5247–5266.
Yiatros, S., and Wadee, M. A. (2011). “Interactive buckling in sandwich beam-columns.” IMA J. Appl. Math., 76(1), 146–168.
Zenkert, D. (1995). An introduction to sandwich construction, Engineering Materials Advisory Services, London.
Zenkour, A. M. (2005). “A comprehensive analysis of functionally graded sandwich plates: Part 1—Deflection and stresses.” Int. J. Solids Struct., 42(18–19), 5224–5242.
Zhu, H., and Sankar, B. V. (2007). “Analysis of sandwich TPS panel with functionally graded foam core by Galerkin method.” Compos. Struct., 77(3), 280–287.
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Published In
Journal of Engineering Mechanics
Volume 139 • Issue 8 • August 2013
Pages: 952 - 960
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jan 31, 2012
Accepted: Jul 27, 2012
Published online: Aug 2, 2012
Published in print: Aug 1, 2013
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