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
Green A.E., Naghdi P.M.: Thermoelasticity without energy dissipation. J. Elast. 31, 189–208 (1993)
Chandrasekharaiah D.S.: Hyperbolic thermoelasticity: a review of recent literature. Appl. Mech. Rev. 51, 705–729 (1998)
Melnik R.V.N.: Discrete models of coupled dynamic thermoelasticity for stress-temperature formulations. Appl. Math. Comput. 122, 107–132 (2001)
Taheri H., Fariborz S., Eslami M.R.: Thermoelastic analysis of an annulus using the Green–Naghdi model. J. Therm. Stress. 28, 911–927 (2005)
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)
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)
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)
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)
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)
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)
Nakonieczny K., Sadowski T.: Modelling of thermal shocks in composite materials using a meshfree FEM. Comput. Mater. Sci. 44, 1307–1311 (2009)
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)
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)
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)
Benito J.J., Urena F., Gavete L.: Influence of several factors in the generalized finite difference method. Appl. Math. Model. 25, 1039–1053 (2001)
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)
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)
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)
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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