Effect of Viscoelastic Interfaces on Thermo-Mechanical Behavior of a Layered Functionally Graded Spherical Vessel

Document Type : Research Article

Authors

1 Mechanical Engineering Department, University of Larestan, Lar, Iran

2 New Technologies Research Center (NTRC), Amirkabir University of Technology, Tehran, Iran

3 Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract

In layered structures, the interface of layers is not always perfect and the analysis of
problems which have imperfect interfaces is of the high level of importance. In this paper, an analytical
approach is used to study the behavior of a layered functionally graded spherical vessel under thermal
and mechanical loadings at the inner and outer surfaces. The interfaces of the layers in the vessel are
considered to be imperfect and a viscoelastic layer of negligible thickness is assumed between any
two layers. The behavior of these viscoelastic layers is modeled by means of Kelvin-Voigt model. In
order to solve the problem, the governing equations of each layer are extracted via the thermoelasticity
theory and by applying the appropriate boundary conditions at the interface of the layers, the overall
displacement and stress fields are found in the vessel and numerical results are presented for different
parameters. The obtained results show that the stiffness of the viscoelastic layer affects the value of the
displacements and the stresses as well as the stabilization time of the system. However, changing the
damping parameter of the Kelvin-Voigt model only changes the stabilization time and not the values of
the displacements and stresses.

Highlights

[1] N. Noda, Thermal stresses in materials with temperature-dependent properties, Appl. Mech. Rev, 44(9) (1991) 383-397.

[2] M.P. Lutz, R.W. Zimmerman, Thermal stresses and effective thermal expansion coefficient of a functionally gradient sphere, Journal of Thermal stresses, 19(1) (1996) 39-54.

[3] N. Tutuncu, M. Ozturk, Exact solutions for stresses in functionally graded pressure vessels, Composites Part B: Engineering, 32(8) (2001) 683-686.

[4] L. You, J. Zhang, X. You, Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials, International Journal of Pressure Vessels and Piping, 82(5) (2005) 347-354.

[5] M. Eslami, M. Babaei, R. Poultangari, Thermal and mechanical stresses in a functionally graded thick sphere, International Journal of Pressure Vessels and Piping, 82(7) (2005) 522-527.

[6] R. Poultangari, M. Jabbari, M. Eslami, Functionally graded hollow spheres under non-axisymmetric thermo-mechanical loads, International Journal of Pressure Vessels and Piping, 85(5) (2008) 295-305.

[7] T. Akis, Elastoplastic analysis of functionally graded spherical pressure vessels, Computational Materials Science, 46(2) (2009) 545-554.

[8] N. Tutuncu, B. Temel, A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres, Composite Structures, 91(3) (2009) 385-390.

[9] M. Jabbari, S. Karampour, M. Eslami, Radially symmetric steady state thermal and mechanical stresses of a poro FGM hollow sphere, ISRN Mechanical Engineering, 2011 (2011).

[10] M.Z. Nejad, M. Abedi, M.H. Lotfian, M. Ghannad, An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties, Journal of Mechanical Science and Technology, 26(12) (2012) 4081-4087.

[11] Y. Bayat, M. Ghannad, H. Torabi, Analytical and numerical analysis for the FGM thick sphere under combined pressure and temperature loading, Archive of Applied Mechanics, 82(2) (2012) 229-242.

[12] W. Chen, J. Cai, G. Ye, Exact solutions of cross-ply laminates with bonding imperfections, AIAA journal, 41(11) (2003) 2244-2250.

[13] W. Chen, K.Y. Lee, Three-dimensional exact analysis of angle-ply laminates in cylindrical bending with interfacial damage via state-space method, Composite Structures, 64(3) (2004) 275-283.

[14] A. Chakrabarti, P. Topdar, A.H. Sheikh, Vibration and buckling of laminated sandwich plates having interfacial imperfections, European Journal of Mechanics-A/Solids, 25(6) (2006) 981-995.

[15] Y. Zhou, W. Chen, C. Lü, Semi-analytical solution for orthotropic piezoelectric laminates in cylindrical bending with interfacial imperfections, Composite Structures, 92(4) (2010) 1009-1018.

[16] S. Kapuria, P.G. Nair, Exact three-dimensional piezothermoelasticity solution for dynamics of rectangular cross-ply hybrid plates featuring interlaminar bonding imperfections, Composites Science and Technology, 70(5) (2010) 752-762.

[17] D.-h. Li, J.-x. Xu, G.-h. Qing, Free vibration analysis and eigenvalues sensitivity analysis for the composite laminates with interfacial imperfection, Composites Part B: Engineering, 42(6) (2011) 1588-1595.

[18] D. Li, Y. Liu, Three-dimensional semi-analytical model for the static response and sensitivity analysis of the composite stiffened laminated plate with interfacial imperfections, Composite Structures, 94(6) (2012) 1943- 1958.

[19] Z. Hashin, Composite materials with viscoelastic interphase: creep and relaxation, Mechanics of Materials, 11(2) (1991) 135-148.

[20] H. Fan, G. Wang, Interaction between a screw dislocation and viscoelastic interfaces, International Journal of Solids and Structures, 40(4) (2003) 763-776.

[21] L. He, J. Jiang, Transient mechanical response of laminated elastic strips with viscous interfaces in cylindrical bending, Composites Science and Technology, 63(6) (2003) 821-828.

[22] W. Chen, K.Y. Lee, Time-dependent behaviors of angle-ply laminates with viscous interfaces in cylindrical bending, European Journal of Mechanics-A/Solids, 23(2) (2004) 235-245.

[23] W. Yan, W.-q. Chen, Time-dependent response of laminated isotropic strips with viscoelastic interfaces, Journal of Zhejiang University-Science A, 5(11) (2004) 1318-1321.

[24] N.J. Pagano, Exact Solutions for Composite Laminates in Cylindrical Bending, Journal of Composite Materials, 3(3) (1969) 398-411.

[25] N.J. Pagano, Influence of Shear Coupling in Cylindrical. Bending of Anisotropic Laminates, Journal of Composite Materials, 4(3) (1970) 330-343.

[26] N.J. Pagano, Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates, Journal of Composite Materials, 4(1) (1970) 20-34.

[27] W. Chen, J. Cai, G. Ye, Responses of cross-ply laminates with viscous interfaces in cylindrical bending, Computer methods in applied mechanics and engineering, 194(6) (2005) 823-835.

[28] W. Chen, G.W. Kim, K.Y. Lee, The effect of viscous interfaces on the bending of orthotropic rectangular laminates, Composite structures, 67(3) (2005) 323-331.

[29] W. Chen, J.P. Jung, G.W. Kim, K.Y. Lee, Cross-ply laminated cylindrical panels with viscous interfaces subjected to static loading, European Journal of Mechanics-A/Solids, 24(5) (2005) 728-739.

[30] W. Yan, J. Ying, W. Chen, The behavior of angle-ply laminated cylindrical shells with viscoelastic interfaces in cylindrical bending, Composite structures, 78(4) (2007) 551-559.

[31] W. Yan, J. Ying, W. Chen, Response of laminated adaptive composite beams with viscoelastic interfaces, Composite structures, 74(1) (2006) 70-79.

[32] W. Yan, W. Chen, Electro-mechanical response of functionally graded beams with imperfectly integrated surface piezoelectric layers, Science in China Series G: Physics Mechanics and Astronomy, 49(5) (2006) 513- 525.

[33] Y. Wei, Y. Ji, C. Weiqiu, A three-dimensional solution for laminated orthotropic rectangular plates with viscoelastic interfaces, Acta Mechanica Solida Sinica, 19(2) (2006) 181-188.

[34] W. Yan, W. Chen, B. Wang, On time-dependent behavior of cross-ply laminated strips with viscoelastic interfaces, Applied mathematical modelling, 31(2) (2007) 381-391.

[35] W. Yan, J. Wang, W. Chen, Cylindrical bending responses of angle-ply piezoelectric laminates with viscoelastic interfaces, Applied Mathematical Modelling, 38(24) (2014) 6018-6030.

[36] A. Alibeigloo, Three-dimensional static and free vibration analysis of laminated cylindrical panel with viscoelastic interfaces, Journal of Composite Materials, 49(19) (2015) 2415-2430.

[37] A. Alibeigloo, Effect of viscoelastic interface on three-dimensional static and vibration behavior of laminated composite plate, Composites Part B: Engineering, 75 (2015) 17-28.

Keywords

References

[1] N. Noda, Thermal stresses in materials with temperature-dependent properties, Appl. Mech. Rev, 44(9) (1991) 383-397.
[2] M.P. Lutz, R.W. Zimmerman, Thermal stresses and effective thermal expansion coefficient of a functionally gradient sphere, Journal of Thermal stresses, 19(1) (1996) 39-54.
[3] N. Tutuncu, M. Ozturk, Exact solutions for stresses in functionally graded pressure vessels, Composites Part B: Engineering, 32(8) (2001) 683-686.
[4] L. You, J. Zhang, X. You, Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials, International Journal of Pressure Vessels and Piping, 82(5) (2005) 347-354.
[5] M. Eslami, M. Babaei, R. Poultangari, Thermal and mechanical stresses in a functionally graded thick sphere, International Journal of Pressure Vessels and Piping, 82(7) (2005) 522-527.
[6] R. Poultangari, M. Jabbari, M. Eslami, Functionally graded hollow spheres under non-axisymmetric thermo-mechanical loads, International Journal of Pressure Vessels and Piping, 85(5) (2008) 295-305.
[7] T. Akis, Elastoplastic analysis of functionally graded spherical pressure vessels, Computational Materials Science, 46(2) (2009) 545-554.
[8] N. Tutuncu, B. Temel, A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres, Composite Structures, 91(3) (2009) 385-390.
[9] M. Jabbari, S. Karampour, M. Eslami, Radially symmetric steady state thermal and mechanical stresses of a poro FGM hollow sphere, ISRN Mechanical Engineering, 2011 (2011).
[10] M.Z. Nejad, M. Abedi, M.H. Lotfian, M. Ghannad, An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties, Journal of Mechanical Science and Technology, 26(12) (2012) 4081-4087.
[11] Y. Bayat, M. Ghannad, H. Torabi, Analytical and numerical analysis for the FGM thick sphere under combined pressure and temperature loading, Archive of Applied Mechanics, 82(2) (2012) 229-242.
[12] W. Chen, J. Cai, G. Ye, Exact solutions of cross-ply laminates with bonding imperfections, AIAA journal, 41(11) (2003) 2244-2250.
[13] W. Chen, K.Y. Lee, Three-dimensional exact analysis of angle-ply laminates in cylindrical bending with interfacial damage via state-space method, Composite Structures, 64(3) (2004) 275-283.
[14] A. Chakrabarti, P. Topdar, A.H. Sheikh, Vibration and buckling of laminated sandwich plates having interfacial imperfections, European Journal of Mechanics-A/Solids, 25(6) (2006) 981-995.
[15] Y. Zhou, W. Chen, C. Lü, Semi-analytical solution for orthotropic piezoelectric laminates in cylindrical bending with interfacial imperfections, Composite Structures, 92(4) (2010) 1009-1018.
[16] S. Kapuria, P.G. Nair, Exact three-dimensional piezothermoelasticity solution for dynamics of rectangular cross-ply hybrid plates featuring interlaminar bonding imperfections, Composites Science and Technology, 70(5) (2010) 752-762.
[17] D.-h. Li, J.-x. Xu, G.-h. Qing, Free vibration analysis and eigenvalues sensitivity analysis for the composite laminates with interfacial imperfection, Composites Part B: Engineering, 42(6) (2011) 1588-1595.
[18] D. Li, Y. Liu, Three-dimensional semi-analytical model for the static response and sensitivity analysis of the composite stiffened laminated plate with interfacial imperfections, Composite Structures, 94(6) (2012) 1943- 1958.
[19] Z. Hashin, Composite materials with viscoelastic interphase: creep and relaxation, Mechanics of Materials, 11(2) (1991) 135-148.
[20] H. Fan, G. Wang, Interaction between a screw dislocation and viscoelastic interfaces, International Journal of Solids and Structures, 40(4) (2003) 763-776.
[21] L. He, J. Jiang, Transient mechanical response of laminated elastic strips with viscous interfaces in cylindrical bending, Composites Science and Technology, 63(6) (2003) 821-828.
[22] W. Chen, K.Y. Lee, Time-dependent behaviors of angle-ply laminates with viscous interfaces in cylindrical bending, European Journal of Mechanics-A/Solids, 23(2) (2004) 235-245.
[23] W. Yan, W.-q. Chen, Time-dependent response of laminated isotropic strips with viscoelastic interfaces, Journal of Zhejiang University-Science A, 5(11) (2004) 1318-1321.
[24] N.J. Pagano, Exact Solutions for Composite Laminates in Cylindrical Bending, Journal of Composite Materials, 3(3) (1969) 398-411.
[25] N.J. Pagano, Influence of Shear Coupling in Cylindrical. Bending of Anisotropic Laminates, Journal of Composite Materials, 4(3) (1970) 330-343.
[26] N.J. Pagano, Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates, Journal of Composite Materials, 4(1) (1970) 20-34.
[27] W. Chen, J. Cai, G. Ye, Responses of cross-ply laminates with viscous interfaces in cylindrical bending, Computer methods in applied mechanics and engineering, 194(6) (2005) 823-835.
[28] W. Chen, G.W. Kim, K.Y. Lee, The effect of viscous interfaces on the bending of orthotropic rectangular laminates, Composite structures, 67(3) (2005) 323-331.
[29] W. Chen, J.P. Jung, G.W. Kim, K.Y. Lee, Cross-ply laminated cylindrical panels with viscous interfaces subjected to static loading, European Journal of Mechanics-A/Solids, 24(5) (2005) 728-739.
[30] W. Yan, J. Ying, W. Chen, The behavior of angle-ply laminated cylindrical shells with viscoelastic interfaces in cylindrical bending, Composite structures, 78(4) (2007) 551-559.
[31] W. Yan, J. Ying, W. Chen, Response of laminated adaptive composite beams with viscoelastic interfaces, Composite structures, 74(1) (2006) 70-79.
[32] W. Yan, W. Chen, Electro-mechanical response of functionally graded beams with imperfectly integrated surface piezoelectric layers, Science in China Series G: Physics Mechanics and Astronomy, 49(5) (2006) 513- 525.
[33] Y. Wei, Y. Ji, C. Weiqiu, A three-dimensional solution for laminated orthotropic rectangular plates with viscoelastic interfaces, Acta Mechanica Solida Sinica, 19(2) (2006) 181-188.
[34] W. Yan, W. Chen, B. Wang, On time-dependent behavior of cross-ply laminated strips with viscoelastic interfaces, Applied mathematical modelling, 31(2) (2007) 381-391.
[35] W. Yan, J. Wang, W. Chen, Cylindrical bending responses of angle-ply piezoelectric laminates with viscoelastic interfaces, Applied Mathematical Modelling, 38(24) (2014) 6018-6030.
[36] A. Alibeigloo, Three-dimensional static and free vibration analysis of laminated cylindrical panel with viscoelastic interfaces, Journal of Composite Materials, 49(19) (2015) 2415-2430.
[37] A. Alibeigloo, Effect of viscoelastic interface on three-dimensional static and vibration behavior of laminated composite plate, Composites Part B: Engineering, 75 (2015) 17-28.
AUT Journal of Mechanical Engineering
Volume 1, Issue 1
June 2017
Pages 75-88

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