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http://dx.doi.org/10.12989/sem.2006.24.4.447

Vibrations and thermal stability of functionally graded spherical caps  

Prakash, T. (Department of Applied Mechanics, Indian Institute of Technology Delhi)
Singh, M.K. (Department of Applied Mechanics, Indian Institute of Technology Delhi)
Ganapathi, M. (Institute of Armament Technology)
Publication Information
Structural Engineering and Mechanics / v.24, no.4, 2006 , pp. 447-461 More about this Journal
Abstract
Here, the axisymmetric free flexural vibrations and thermal stability behaviors of functionally graded spherical caps are investigated employing a three-noded axisymmetric curved shell element based on field consistency approach. The formulation is based on first-order shear deformation theory and it includes the in-plane and rotary inertia effects. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. The effective material properties are evaluated using homogenization method. A detailed numerical study is carried out to bring out the effects of shell geometries, power law index of functionally graded material and base radius-to-thickness on the vibrations and buckling characteristics of spherical shells.
Keywords
functionally graded; vibration; spherical shell; thermal buckling; power law index;
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1 Benveniste, Y. (1987), 'A new approach to the application of Mori-Tanaka's theory in composite materials', Mech. Mater., 6, 147-157   DOI   ScienceOn
2 Kadoli, R. and Ganesan, N. (2005), 'A theoretical analysis of linear thermoelastic buckling of composite hemispherical shells with a cut-out at the apex', Compos. Struct., 68, 87-101   DOI   ScienceOn
3 Dao, M., Gu, P., Maeqal, A. and Asaro, R. (1997), 'A micro mechanical study of a residual stress in functionally graded materials', Acta Materialia, 45, 3265-3276   DOI   ScienceOn
4 Durodola, J.F. and Adlington, J.E. (1996), 'Functionally graded material properties for disks and rotors', Proc. 1st Int. Conf. on Ceramic and Metal Matrix Composites, San Sebastian, Spain
5 Fukui, Y. (1991), 'Fundamental investigation of functionally gradient material manufacturing system using centrifugal force', JSME Int. J Series III, 34, 144-148
6 Ganapathi, M., Gupta, S.S. and Patel, B.P. (2003), 'Nonlinear axisymmetric dynamic buckling of laminated angle-ply composite spherical caps', Compos. Struct., 59, 89-97   DOI   ScienceOn
7 Hatta, H. and Taya, M. (1985), 'Effective thermal conductivity of a misoriented short fiber composite', J. Appl. Phy., 58, 2478-2486   DOI
8 He, XQ., Ng, T.Y., Sivashanker, S. and Liew, KM. (2001), 'Active control of FGM plates with integrated piezoelectric sensors and actuators', Int. J. Solids Struct., 38, 1641-1655   DOI   ScienceOn
9 Koizumi, M. (1993), 'The concept of FGM', Ceramic Transactions Functionally Graded Material, 34, 3-10
10 Koizumi, M. (1997), 'FGM activities in Japan', Composites Part B: Engineering, 28, 1-4   DOI   ScienceOn
11 Kraus, H. (1967), Thin Elastic Shells, New York, John Wiley
12 Li, C., Weng, Z. and Duan, Z. (2001), 'Dynamic stress intensity factor of a functionally graded material with a finite crack under anti-plane shear loading', Acta Mechanica., 149, 1-10   DOI   ScienceOn
13 Loy, CT., Lam, KY. and Reddy, J.N. (1999), 'Vibration of functionally graded cylindrical shells', Int. J. Mech. Sci., 41, 309-324   DOI   ScienceOn
14 Ma, L.S. and Wang, T.J. (2003), 'Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings', Int. J. Solids Struct., 40, 3311-3330   DOI   ScienceOn
15 Ng, TY., He, X.Q. and Liew, KM. (2002), 'Finite element modeling of active control of functionally graded shells in frequency domain via piezoelectric sensors and actuators', Comput. Mech., 28, 1-9   DOI
16 Ng, TY., Lam, K.Y. and Liew, KM. (2000), 'Effects of FGM materials on the parametric resonance of plate structures', Comput. Meth. Appl. Mech. Eng., 190,953-962   DOI   ScienceOn
17 Ng, TY., Lam, K.Y., Liew, KM. and Reddy, N.J. (2001), 'Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading', Int. J. Solids Struct., 38, 1295-1309   DOI   ScienceOn
18 Obata, Y. and Noda, N. (1994), 'Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material', J. Thermal Stresses, 17, 471-487   DOI   ScienceOn
19 Praveen, GN. and Reddy, IN. (1998), 'Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates', Int. J. Solids Struct., 35, 4457-4476   DOI   ScienceOn
20 Oh, Sang-Yong, Librescu, Liviu and Song, Ohseop (2003), 'Thin-walled rotating blades made of functionally graded materials: Modelling and vibration analysis', AIAA-2003-1541 44th AIAA/ASME/ASCE/AHS/ASC Structures Structural Dynamics and Materials Conference, Norfolk, Virginia
21 Qian, L.E, Batra, R.C. and Chen, L.M. (2004), 'Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local PetrovGalerkin method', Composites Part B: Engineering, 35, 685-697   DOI   ScienceOn
22 Suresh, S. and Mortensen, A. (1998), 'Fundamentals of functionally graded materials', Institute of Materials, London
23 Takezono, S., Tao, K, lnamura, E. and Inoue, M. (1994), 'Thermal stress and deformation in functionally graded material shells of revolution under thermal loading due to fluid', JSME Int. Series A: Mechanics and Material Engineering, 39, 573-581
24 Vel, S.S. and Batra, R.C. (2004), 'Three-dimensional exact solution for the vibration of functionally graded rectangular plates', J Sound Vib., 272, 703-730   DOI   ScienceOn
25 Weisenbek, E., Pettermann, RE. and Suresh, S. (1997), 'Elasto-plastic deformation of compositionally graded metal-ceramic composites', Acta Materialia, 45,3401-3417   DOI   ScienceOn
26 Wetherhold, R.c., Seelman, S. and Wang, J.Z. (1996), 'The use of functionally graded materials to eliminate or control thermal deformation', Comp. Sci. Tech., 56, 1099-1104   DOI   ScienceOn
27 Yamaoka, H., Yuki, M., Tahara, K., Irisawa, T., Watanabe, R. and Kawasaki, A. (1993), 'Fabrication of functionally gradient material by slurry stacking and sintering process', Ceramic Transactions Functionally Gradient Material, 34, 165-172
28 Zienkiewicz, O.C. and Taylor, R.L. (1989), The Finite Element Method, McGraw-Hill, Singapore
29 Yang, J., Kitipomchai, S. and Liew, K.M. (2003), 'Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates', Comput. Meth. Appl. Mech. Eng., 192,3861-3885   DOI   ScienceOn
30 Zhang, c., Savaids, A., Savaids, G and Zhu, H. (2003), 'Transient dynamic analysis of a cracked functionally graded material by BIEM', Comput. Mater. Sci., 26, 167-174   DOI   ScienceOn
31 Prathap, G and Ramesh Babu, C. (1986), 'A field-consistent three-noded quadratic curved axisymmetric shell element', Int. J. Numer. Meth. Eng., 23, 711-723   DOI   ScienceOn
32 Mori, T and Tanaka, K (1973), 'Average stress in matrix and average elastic energy of materials with misfitting inclusions', Acta Metallurgica, 21, 571-574   DOI   ScienceOn
33 Tauchert, T.R. (1991), 'Thermally induced flexure, buckling and vibration of plates', Appl. Mech. Rev., 44, 347-360   DOI
34 Lanhe, Wu (2004), 'Thermal buckling of a simply supported moderately thick rectangular FGM plate', Compos. Struct., 64, 211-218   DOI   ScienceOn
35 Rosen, B.w. and Hashin, Z. (1970), 'Effective thermal expansion coefficients and specific heats of composite materials', Int. J Eng. Sci., 8, 157-173   DOI   ScienceOn
36 Cheng, Z.-Q. and Batra, R.C. (2000), 'Three-dimensional thermoelastic deformations of a functionally graded elliptic plate', Composites Part B : Engineering, 31, 97-106   DOI   ScienceOn
37 Li, C., Weng, Z. and Duan, Z. (2001), 'Dynamic behavior of a cylindrical crack in a functionally graded interlayer under torsional loading', Int. J. Solids Struct., 38, 7473-7485   DOI   ScienceOn
38 Sathyamoorthy, M. (1994), 'Vibrations of moderately thick shallow spherical shells at large amplitudes', J. Sound Vib., 172, 63-70   DOI   ScienceOn
39 Makino, A., Araki, N., Kitajima, H. and Ohashi, K (1994), 'Transient temperature response of functionally gradient material subjected to partial, stepwise heating', Trans. JSME, Part B, 60, 4200-4206   DOI