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Shock-induced thermoelastic wave propagation analysisin a thick hollow cylinder without energy dissipation using mesh-free generalized finite difference (GFD) method

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Abstract

The main objective of this article is the exploitation of the generalized finite difference method to study the thermoelastic wave propagation, that is, the dynamic behaviors of displacement and temperature field in a thick hollow cylinder. The thermoelasticity governing equations are derived based on Green–Naghdi coupled thermoelasticity theory (without energy dissipation). The generalized finite difference (GFD) method is used to approximate the space variables, and Newmark finite difference (NFD) is employed to obtain the behaviors of parameters in time domain. The time histories of displacement and temperature fields across the thickness of the cylinder are obtained and the propagations of thermal and elastic waves are illustrated at various times. Using the GFD method, the wave front in temperature and elastic domains can be tracked, and the comparison between results based on GFD and other numerical methods shows very good agreement. The application of GFD method in coupled thermoelasticity problems has a high capability because it does not require a mesh generation. A comparison between the presented mesh-free GFD method and meshless local Petrov–Galerkin (MLPG) method shows a good agreement of the results.

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References

  1. Green A.E., Naghdi P.M.: Thermoelasticity without energy dissipation. J. Elast. 31, 189–208 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chandrasekharaiah D.S.: Hyperbolic thermoelasticity: a review of recent literature. Appl. Mech. Rev. 51, 705–729 (1998)

    Article  Google Scholar 

  3. Melnik R.V.N.: Discrete models of coupled dynamic thermoelasticity for stress-temperature formulations. Appl. Math. Comput. 122, 107–132 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Taheri H., Fariborz S., Eslami M.R.: Thermoelastic analysis of an annulus using the Green–Naghdi model. J. Therm. Stress. 28, 911–927 (2005)

    Article  Google Scholar 

  5. Hosseini S.M., Akhlaghi M., Shaker M.: Heat conduction and heat wave propagation in functionally graded thick hollow cylinder based on coupled thermoelasticity without energy dissipation. Heat Mass Transf. 44, 1477–1484 (2008)

    Article  Google Scholar 

  6. Hosseini S.M.: Coupled thermoelasticity and second sound in finite length functionally graded thick hollow cylinders (without energy dissipation). Mater. Des. 30, 2011–2023 (2009)

    Article  Google Scholar 

  7. Hosseini S.M., Shahabian F.: Transient analysis of thermo-elastic waves in thick hollow cylinders using a stochastic hybrid numerical method, considering Gaussian mechanical properties. Appl. Math. Model. 35, 4697–4714 (2011)

    Article  MATH  Google Scholar 

  8. Safari A., Tahani M., Hosseini S.M.: Two-dimensional dynamic analysis of thermal stresses in a finite-length FG thick hollow cylinder subjected to thermal shock loading using an analytical method. Acta Mech. 220, 299–314 (2011)

    Article  MATH  Google Scholar 

  9. Hosseini S.M., Abolbashari M.H.: Analytical solution for thermoelastic waves propagation analysis in thick hollow cylinder based on Green–Naghdi model of coupled thermoelasticity. J. Therm. Stress. 35, 363–376 (2012)

    Article  Google Scholar 

  10. Sladek J., Sladek V., Hellmich Ch., Eberhardsteiner J.: Heat conduction analysis of 3D axisymmetric and anisotropic FGM bodies by meshless local Petrov–Galerkin method. Comput. Mech. 39, 323–333 (2007)

    Article  MATH  Google Scholar 

  11. Nakonieczny K., Sadowski T.: Modelling of thermal shocks in composite materials using a meshfree FEM. Comput. Mater. Sci. 44, 1307–1311 (2009)

    Article  Google Scholar 

  12. Sladek J., Sladek V., Tan C.L., Atluri S.N.: Analysis of transient heat conduction in 3D anisotropic functionally graded solids. Comput. Model. Eng. Sci. (CMES) 32, 161–174 (2008)

    MathSciNet  MATH  Google Scholar 

  13. Hosseini S.M., Sladek J., Sladek V.: Meshless local Petrov–Galerkin method for coupled thermo-elasticity analysis of a functionally graded thick hollow cylinder. Eng. Anal. Boundary Elem. 35, 827–835 (2011)

    Article  MathSciNet  Google Scholar 

  14. Hosseini S.M., Shahabian F., Sladek J., Sladek V.: Stochastic meshless local Petrov–Galerkin (MLPG) method for thermo-elastic wave propagation analysis in functionally graded thick hollow cylinders. Comput. Model. Eng. Sci. (CMES) 71, 39–66 (2011)

    MathSciNet  MATH  Google Scholar 

  15. Benito J.J., Urena F., Gavete L.: Influence of several factors in the generalized finite difference method. Appl. Math. Model. 25, 1039–1053 (2001)

    Article  MATH  Google Scholar 

  16. Benito J.J., Urena F., Gavete L.: An h-adaptive method in the generalized finite differences. Comput. Methods Appl. Mech. Eng. 192, 735–739 (2003)

    Article  MATH  Google Scholar 

  17. Gavete L., Benito J.J., Gavete M.L.: Improvements of generalized finite difference method and comparison with other meshless method. Appl. Math. Model. 27, 831–847 (2003)

    Article  MATH  Google Scholar 

  18. Benito J.J., Urena F., Gavete L.: Solving parabolic and hyperbolic equations by the generalized finite difference method. J. Comput. Appl. Math. 209, 208–233 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Industrial Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran

    Seyed Mahmoud Hosseini

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  1. Seyed Mahmoud Hosseini
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Correspondence to Seyed Mahmoud Hosseini.

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Hosseini, S.M. Shock-induced thermoelastic wave propagation analysisin a thick hollow cylinder without energy dissipation using mesh-free generalized finite difference (GFD) method. Acta Mech 224, 465–478 (2013). https://doi.org/10.1007/s00707-012-0773-2

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  • DOI: https://doi.org/10.1007/s00707-012-0773-2

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