The instability of functionally graded material (FGM) structures is one of the major threats to their service safety in engineering applications. This paper aims to clarify a long-standing controversy on the thermal instability type of simply-supported FGM beams. First, based on the Euler-Bernoulli beam theory and von Kármán geometric nonlinearity, a nonlinear governing equation of simply-supported FGM beams under uniform thermal loads by Zhang's two-variable method is formulated. Second, an approximate analytic solution to the nonlinear integro-differential boundary value problem under a thermal-induced inhomogeneous force boundary condition is obtained by using a semiinverse method when the coordinate axis is relocated to the bending axis (physical neutral plane), and then the analytical predictions are verified by the differential quadrature method (DQM). Finally, based on the free energy theorem, it is revealed that the symmetry breaking caused by the material inhomogeneity can make the simply-supported FGM beam under uniform thermal loads occur snap-through postbuckling only in odd modes; furthermore, the nonlinear critical load of thermal buckling varies non-monotonically with the functional gradient index due to the stretching-bending coupling effect. These results are expected to provide new ideas and references for the design and regulation of FGM structures.
Yongyong XI, Qiang LYU, Nenghui ZHANG, Junzheng WU
. Thermal-induced snap-through buckling of simply-supported functionally graded beams[J]. Applied Mathematics and Mechanics, 2020
, 41(12)
: 1821
-1832
.
DOI: 10.1007/s10483-020-2691-7
[1] YUAN, Y., ZHAO, K., SAHMANI, S., and SAFAEI, B. Size-dependent shear buckling response of FGM skew nanoplates modeled via different homogenization schemes. Applied Mathematics and Mechanics (English Edition), 41(4), 587-604(2020) https://doi.org/10.1007/s10483-020-2600-6
[2] LI, S. R. and FAN, L. L. Free vibration of FGM Timoshenko beams with through-width delamination. Science China-Physics Mechanics and Astronomy, 57, 927-934(2014)
[3] AMIRI, A., MOHAMMADIMEHR, M., and ANVARI, M. Stress and buckling analysis of a thickwalled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite (CNTRC) face sheets. Applied Mathematics and Mechanics (English Edition), 41(9), 1027-1038(2020) https://doi.org/10.1007/s10483-020-2627-7
[4] KIANI, Y. and ESLAMI, M. R. Thermal buckling analysis of functionally graded material beams. International Journal of Mechanics and Materials in Design, 6, 229-238(2010)
[5] WATTANASAKULPONG, N., PRUSTY, B. G., and KELLY, D. W. Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams. International Journal of Mechanical Sciences, 53, 734-743(2011)
[6] SHEN, H. S., LIN. F., and XIANG, Y. Nonlinear bending and thermal postbuckling of functionally graded graphene-reinforced composite laminated beams resting on elastic foundations. Engineering Structures, 140, 89-97(2017)
[7] ESFAHANI, S. E., KIANI, Y., and ESLAMI, M. R. Non-linear thermal stability analysis of temperature dependent FGM beams supported on non-linear hardening elastic foundations. International Journal of Mechanical Sciences, 69, 10-20(2013)
[8] SUN, Y., LI, S. R., and BATRA, R. C. Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation. Journal of Thermal Stresses, 39, 11-26(2016)
[9] QATU, M. S. and LEISSA, A. W. Buckling or transverse deflections of unsymmetrically laminated plates subjected to in-plane loads. AIAA Journal, 31, 189-194(1993)
[10] KIANI, Y. Thermal postbuckling of temperature-dependent sandwich beams with carbon nanotube-reinforced face sheets. Journal of Thermal Stresses, 39, 1098-1110(2016)
[11] AMABILI, M. Nonlinear damping in nonlinear vibrations of rectangular plates:derivation from viscoelasticity and experimental validation. Journal of the Mechanics and Physics of Solids, 118, 275-292(2018)
[12] LEISSA, A. W. Conditions for laminated plates to remain flat under inplane loading. Composite Structures, 6, 261-270(1986)
[13] FANG, W. and WICKERT, J. A. Post buckling of micromachined beams. Journal of Micromechanics and Microengineering, 4, 116-122(1994)
[14] ZHANG, N. H. and CHEN, J. Z. An alternative two-variable model for bending problems of multilayered beams. Journal of Applied Mechanics, 75, 1-3(2008)
[15] HSUEH, C. H. and LEE, S. Modeling of elastic thermal stresses in two materials joined by a graded layer. Composites Part B:Engineering, 34, 747-752(2003)
[16] ZHANG, D. G. and ZHOU, Y. H. A theoretical analysis of FGM thin plates based on physical neutral surface. Computational Materials Science, 44, 716-720(2008)
[17] EMAM, S. A. and NAYFEH, A. H. Postbuckling and free vibrations of composite beams. Composite Structures, 88, 636-642(2009)
[18] QIAN, W. C. Variational Method and Finite Element Method, China Science Press, Beijing, 535-544(1980)
[19] MAO, L. J. and MA, L. S. Nonlinear static responses of FGM beams under non-uniform thermal loading (in Chinese). Engineering Mechanics, 34, 1-8(2017)
[20] LYU, Q., LI, J. J., and ZHANG, N. H. Quasi-static and dynamical analyses of a thermoviscoelastic Timoshenko beam using the differential quadrature method. Applied Mathematics and Mechanics (English Edition), 40(4), 549-562(2019) https://doi.org/10.1007/s10483-019-2470-8
[21] MIRZAEI, M. and KIANI, Y. Snap-through phenomenon in a thermally postbuckled temperature dependent sandwich beam with FG-CNTRC face sheets. Composite Structures, 134, 1004-1013(2015)
[22] YANG, Y. H. and CHEN, Y. Y. Elastic stability equations for thin walled curved beam with biaxially symmetric cross section (in Chinese). Chinese Quarterly of Mechanics, 27, 387-396(2006)
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