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http://dx.doi.org/10.12989/sem.2013.45.3.355

Axisymmetrical bending of single- and multi-span functionally graded hollow cylinders  

Bian, Z.G. (Ningbo Institute of Technology, Zhejiang University)
Wang, Y.H. (Ningbo Institute of Technology, Zhejiang University)
Publication Information
Structural Engineering and Mechanics / v.45, no.3, 2013 , pp. 355-371 More about this Journal
Abstract
Single- and multi-span orthotropic functionally graded hollow cylinders subjected to axisymmetrical bending are investigated on the basis of a unified shear deformable shell theory, in which the transverse displacement is expressed by means of a general shape function. To approach the through-thickness inhomogeneity of the hollow cylinder, a laminated model is employed. The shape function therefore shall be determined for each fictitious layer. To improve the computational efficiency, we resort to a transfer matrix method. Based on the principle of minimum potential energy, equilibrium equations are established, which are then solved analytically using the transfer matrix method for arbitrary boundary conditions. Numerical comparisons among a third-order shear deformable shell theory, an exact elastic theory and the present theory are provided for a simply supported hollow cylinder, from which the present theory turns out to be superior in stress estimation. Distributions of displacements and stresses in single- and three-span hollow cylinders with different boundary conditions are also illustrated in numerical examples.
Keywords
axisymmetrical bending; multi-span; hollow cylinder; functionally graded material; unified shear deformable shell theory; transfer matrix method;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 Abrate, S. and Foster, E. (1995), "Vibrations of composite plates with intermediate line supports", J. Sound. Vib., 179, 793-815.   DOI   ScienceOn
2 Andrews, M.G., Massabo, R., Cavicchi, A. and Cox, B.N. (2009), "Dynamic interaction effects of multiple delaminations in plates subject to cylindrical bending", Int. J. Solid. Struct., 46, 1815-1833.   DOI   ScienceOn
3 Aghdam, M.M., Shahmansouri, N. and Bigdeli, K. (2011), "Bending analysis of moderately thick functionally graded conical panels", Compos. Struct., 93, 1376-1384.   DOI   ScienceOn
4 Bahtui, A. and Eslami, M.R. (2007), "Coupled thermoelasticity of functionally graded cylindrical shells", Mech. Res. Comm., 34, 1-18.   DOI   ScienceOn
5 Bian, Z.G., Chen, W.Q., Lim, C.W. and Zhang, N. (2005), "Analytical solutions for single- and multi-span functionally graded plates in cylindrical bending", Int. J. Solid. Struct., 42, 6433-6456.   DOI   ScienceOn
6 Bian, Z.G., Chen, W.Q. and Zhao, J. (2010), "Steady-state response and free vibration of an embedded imperfect smart functionally graded hollow cylinder filled with compressible fluid", Struct. Eng. Mech., 34, 449-474.   DOI   ScienceOn
7 Bian, Z.G., Lim, C.W. and Chen, W.Q. (2006a), "On functionally graded beams with integrated surface piezoelectric layers", Compos. Struct., 72, 339-351.   DOI   ScienceOn
8 Bian, Z.G., Ying, J., Chen, W.Q. and Ding, H.J. (2006b), "Bending and free vibration analysis of a smart functionally graded plate", Struct. Eng. Mech., 23, 97-113.   DOI   ScienceOn
9 Chen, W.Q., Bian, Z.G. and Ding, H.J. (2003), "Three-dimensional analysis of a thick FGM rectangular plate in thermal environment", Journal of Zhejiang University SCIENCE A, 4, 1-7.   DOI   ScienceOn
10 Chen, W.Q., Bian, Z.G. and Ding, H.J. (2004), "Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells", Int. J. Mech. Sci., 46, 159-171.   DOI   ScienceOn
11 Cheung, Y.K. and Zhou, D. (1999), "Eigenfrequencies of tapered rectangular plates with intermediate line supports", Int. J. Solid. Struct., 36, 143-166.   DOI   ScienceOn
12 Cheung, Y.K. and Zhou, D. (2000), "Vibrations of rectangular plates with elastic intermediate line-supports and edge constraints", Thin-Walled Structures, 37, 305-331.   DOI   ScienceOn
13 Cheung, Y.K. and Zhou, D. (2001), "Vibration analysis of symmetrically laminated rectangular plates with intermediate line supports", Comput. Struct., 79, 33-41.   DOI   ScienceOn
14 Huang, S.C. and Hsu, B.S. (1993), "Modal analysis of a spinning cylindrical shell with interior point or circular line supports", J. Vib. Acoust., 115, 535-543.   DOI   ScienceOn
15 Lee, H.P. and Ng, T.Y. (1995), "Dynamic stability of a plate on multiple line and point supports subject to pulsating conservative in-plane loads", J. Sound. Vib., 185, 345-356.   DOI   ScienceOn
16 Li, Q.S. (2003), "An exact approach for free vibration analysis of rectangular plates with line-concentrated mass and elastic line-support", In.t J. Mech. Sci., 45, 669-685.   DOI   ScienceOn
17 Li, S.R., Fu, X.H. and Batra, R.C. (2010), "Free vibration of three-layer circular cylindrical shells with functionally graded middle layer", Mech. Res. Comm., 37, 577-580.   DOI   ScienceOn
18 Liew, K. M., Kitipornchai S. and Xiang, Y. (1995), "Vibration of annular sector Mindlin plates with internal radial line and circumferential arc supports", J. Sound. Vib., 183, 401-419.   DOI   ScienceOn
19 Loy, C.T., Lam, K. Y. and Reddy, J. N. (1999), "Vibration of functionally graded cylindrical shells", Int. J. Mech. Sci., 41, 309-324.   DOI   ScienceOn
20 Matsunaga, H. (2009), "Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory", Compos. Struct., 88, 519-531.   DOI   ScienceOn
21 Miyamoto, Y., Kaysser, W.A., Brain, B.H., Kawasaki, A. and Ford, R.G. (1999), Functionally graded materials: design, processing, and applications, Kluwer Academic Publishers, Dordrecht, Netherlands.
22 Müller, E., Drašar, Č., Schilz, J. and Kaysser, W.A. (2003), "Functionally graded materials for sensor and energy applications", Mater. Sci. Eng., 362, 17-39.   DOI   ScienceOn
23 Na, K.S. and Kim J.H. (2009), "Optimization of volume fractions for functionally graded panels considering stress and critical temperature", Compos. Struct., 89, 509-516.   DOI   ScienceOn
24 Kadoli, R., Akhtar, K., and Ganesan, N. (2008), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Model., 32, 2509-2525.   DOI   ScienceOn
25 Koizumi, M. (1997), "FGM activities in Japan", Compos. B. Eng., 28, 1-4.   DOI   ScienceOn
26 Kokini, K., DeJonge, J., Rangaraj, S. and Beardsley, B. (2002), "Thermal shock of functionally graded thermal barrier coatings with similar thermal resistance", Surf. Coating. Tech., 154, 223-231.   DOI   ScienceOn
27 Kong, J. and Cheung, Y.K. (1995), "Vibration of shear-deformable plates with intermediate line supports: a finite layer approach", J. Sound. Vib., 184, 639-649.   DOI   ScienceOn
28 Pompe, W., Worch, H., Epple, M., Friess, W., Gelinsky, M., Greil, P., Hempel, U., Scharnweber, D. and Schulte, K. (2003), "Functionally graded materials for biomedical applications", Mater. Sci. Eng., 362, 40-60.   DOI   ScienceOn
29 Pradhan, S.C., Loy, C.T., Lam, K.Y. and Reddy, J.N. (2000), "Vibration characteristics of functionally graded cylindrical shells under various boundary conditions", Appl. Acoust., 61, 111-129.   DOI   ScienceOn
30 Qian, X.P. and Dutta, D. (2003), "Design of heterogeneous turbine blade", Comput. Aided. Des., 35, 319-329.   DOI   ScienceOn
31 Soldatos, K.P. and Timarci, T. (1993), "A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories", Compos. Struct., 25, 165-171.   DOI   ScienceOn
32 Soldatos, K.P. and Watson, P. (1997), "A method for improving the stress analysis performance of one- and two-dimensional theories for laminated composites", Acta. Mech., 123, 163-186.   DOI   ScienceOn
33 Vel, S.S. (2010), "Exact elasticity solution for the vibration of functionally graded anisotropic cylindrical shells", Compos. Struct., 92, 2712-2727.   DOI   ScienceOn
34 Veletsos, A.S. and Newmark, N.M. (1956), "Determination of natural frequencies of continuous plates hinged along two opposite edges", J. Appl. Mech., 23, 97-102.
35 Watari, F., Yokoyama, A., Omori, M., Hirai, T., Kondo, H., Uo, M. and Kawasaki, T. (2004), "Biocompatibility of materials and development to functionally graded implant for bio-medical application", Compos. Sci. Tech., 64, 893-908.   DOI   ScienceOn
36 Woodward, B. and Kashtalyan, M. (2011), "Three-dimensional elasticity solution for bending of transversely isotropic functionally graded plates", Eur. J. Mech. Solid., 30, 705-718.   DOI   ScienceOn
37 Wu, L.H., Jiang, Z.Q. and Liu, J. (2005), "Thermoelastic stability of functionally graded cylindrical shells", Compos. Struct., 70, 60-68.   DOI   ScienceOn
38 Xiang, Y., Zhao, Y.B. and Wei, G.W. (2002a), "Exact solutions for vibration of multi-span rectangular Mindlin plates", J. Vib. Acoust., 124, 545-551.   DOI   ScienceOn
39 Xiang, Y., Zhao, Y.B. and Wei, G.W. (2002b), "Levy solutions for vibration of multi-span rectangular plates", In.t J. Mech. Sci., 44, 1195-1218.   DOI   ScienceOn
40 Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Thermoelastic and vibration analysis of functionally graded cylindrical shells", Int. J. Mech. Sci., 51, 694-707.   DOI   ScienceOn
41 Zhou, D. (1994), "Eigenfrequencies of line supported rectangular plates". Int. J. Solid. Struct., 31, 347-358.   DOI   ScienceOn