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Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading. (English) Zbl 1397.74157

Summary: In this paper a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to impact internal pressure is considered. The axisymmetric conditions are assumed for the 2D-FG cylinder. The finite element method with graded material properties within each element is used to model the structure, and the Newmark direct integration method is implemented to solve the time-dependent equations. The time histories of displacements, stresses and 2D wave propagation are investigated for various values of volume fraction exponents. Also the effects of mechanical properties distribution in radial and axial direction on the time responses of the FG cylinder as well as the stress distribution are studied and compared with a cylinder made of 1D-FGM. The achieved results show that using 2D-FGM leads to a more flexible design. To verify the presented method and data, the results are compared to published data.

MSC:

74M20 Impact in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74E05 Inhomogeneity in solid mechanics
Full Text: DOI

References:

[1] Koizumi M.: The concept of FGM. Ceram. Trans. Funct. Graded Mater. 34, 3–10 (1993)
[2] Liu G.R., Han X., Lam K.Y. : Stress waves in functionally gradient materials and its use for material characterization. Compos. Part B Eng. 30, 383–394 (1999) · doi:10.1016/S1359-8368(99)00010-4
[3] Chiu T.C., Erdogan F.: One-dimensional wave propagation in a functionally graded elastic medium. J. Sound Vib. 222, 453–487 (1999) · doi:10.1006/jsvi.1998.2065
[4] Bruck H.A.: A one-dimensional model for designing functionally graded materials to manage stress waves. Int. J. Solids Struct. 37, 6383–6395 (2000) · Zbl 0996.74045 · doi:10.1016/S0020-7683(99)00236-X
[5] Li Y., Ramesh K.T., Chin E.S.C.: Dynamic characterization of layered and graded structures under impulsive loading. Int. J. Solids Struct. 38, 6045–6061 (2001) · Zbl 1075.74566 · doi:10.1016/S0020-7683(00)00364-4
[6] Han X., Liu G.R., Lam K.Y.: Transient waves in plates of functionally graded materials. Int. J. Numer. Methods Eng. 52, 851–865 (2001) · Zbl 1017.74035 · doi:10.1002/nme.237
[7] Berezovski A., Engelbrecht J., Maugin G.A.: Numerical simulation of two-dimensional wave propagation in functionally graded materials. Eur. J. Mech. A Solids 22, 257–265 (2001) · Zbl 1038.74575 · doi:10.1016/S0997-7538(03)00029-9
[8] Batra R.C., Ching H.K.: Analysis of elastodynamic deformations near a crack-notch tip by the meshless local Petrov–Galerkin (MLPG) method. Comput. Model. Eng. Sci. 3, 717–730 (2002) · Zbl 1152.74343
[9] Zhang G.M., Batra R.C.: Wave propagation in functionally graded materials by modified smoothed particle hydrodynamics (MSPH) method. J. Comput. Phys. 222, 374–390 (2007) · Zbl 1108.74032 · doi:10.1016/j.jcp.2006.07.028
[10] Shakeri M., Akhlaghi M., Hoseini S.M.: Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder. Compos. Struct. 76, 174–181 (2006) · doi:10.1016/j.compstruct.2006.06.022
[11] Hosseini M., Akhlaghi M., Shakeri M.: Dynamic response and radial wave propagations of functionally graded thick hollow cylinder. Eng. Comput. 24, 288–303 (2007) · Zbl 1198.74034 · doi:10.1108/02644400710735043
[12] Nemat-Alla M.: Reduction of thermal stresses by developing twodimensional functionally graded materials. Int. J. Solids Struct. 40, 7339–7356 (2003) · Zbl 1063.74506 · doi:10.1016/j.ijsolstr.2003.08.017
[13] Dhaliwal R.S., Singh B.M.: On the theory of elasticity of a non-homogeneous medium. J. Elast. 8, 211–219 (1978) · Zbl 0372.73015 · doi:10.1007/BF00052484
[14] Clements D.L., Budhi W.S.: A boundary element method for the solution of a class of steady-state problems for anisotropic media. Heat Transf. 121, 462–465 (1999) · doi:10.1115/1.2826000
[15] Abudi J., Pindera M.J.: Thermoelastic theory for the response of materials functionally graded in two directions. Int. J. Solids Struct. 33, 931–966 (1996) · Zbl 0926.74008 · doi:10.1016/0020-7683(95)00084-4
[16] Cho J.R., Ha D.Y.: Optimal tailoring of 2D volume-fraction distributions for heat-resisting functionally graded materials using FDM. Comput. Methods Appl. Mech. Eng. 191, 3195–3211 (2002) · Zbl 1101.74372 · doi:10.1016/S0045-7825(02)00256-6
[17] Hedia H.S., Midany T.T., Shabara M.A.N., Fouda N.: Development of cementless metal-backed acetabular cup prosthesis using functionally graded material. Int. J. Mech. Mater. Des. 2, 259–267 (2005)
[18] Santare M.H., Thamburaj P., Gazonas A.: The use of graded finite elements in the study of elastic wave propagation in continuously non-homogeneous materials. Int. J. Solids Struct. 40, 5621–5634 (2003) · Zbl 1059.74551 · doi:10.1016/S0020-7683(03)00315-9
[19] Banks Sills L., Eliasi R., Berlin Y.: Modeling of functionally graded materials in dynamic analyses. Compos. Part B. Eng. 33, 7–15 (2002) · doi:10.1016/S1359-8368(01)00057-9
[20] Scheidler, M.J., Gazonas, G.A.: Analytical and computational study of one-dimensional impact of graded elastic solids. In: Furnish, M.D. et al. (eds.) Shock Compression of Condensed Materials, pp. 689–692 (AIP CP620), Melville, NY, 2001. American Institute of Physics, Woodbury (2002)
[21] Santare M.H., Lambros J.: Use of a graded finite element to model the behavior of nonhomogeneous materials. J. Appl. Mech. 67, 819–822 (2000) · Zbl 1110.74660 · doi:10.1115/1.1328089
[22] Kim J.H., Paulino G.H.: Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials. J. Appl. Mech. 69, 502–514 (2002) · Zbl 1110.74509 · doi:10.1115/1.1467094
[23] Zienkiewicz O.C., Taylor R.L.: The Finite Element Method, VII: Solid Mechanics, 5th edn. Butterworth-Heinemann, Oxford (2000) · Zbl 0991.74003
[24] Shao Z.S.: Mechanical and thermal stresses of a functionally graded circular hollow cylinder with finite length. Int. J. Press. Vess. Pip. 82, 155–163 (2005) · doi:10.1016/j.ijpvp.2004.09.007
[25] Goupee A.J., Vel S.S.: Two-dimensional optimization of material composition of functionally graded materials using meshless analyses and a genetic algorithm. Comput. Methods Appl. Mech. Eng. 195, 5926–5948 (2006) · Zbl 1145.74031 · doi:10.1016/j.cma.2005.09.017
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