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In this paper, the thermoelastic behavior of cylindrical sandwich shell with functionally graded (FGM) core under thermal shock is presented. Thermo mechanical properties of FGM layer are assumed to be independent of temperature and also, very continuously and smoothly functions in the radial direction as a nonlinear power function. The analytical solutions of governing partial differential equations for each layer of cylinder are solved by using Laplace transform and power series method. Mechanical boundary conditions and continuity equations for interfaces are used to obtain unknown parameters that get in recurrence equations for each layer of cylinder. The results in Laplace domain transferred to time domain by employing the fast inverse Laplace transform method (FLIT).The effects of FGM’s power on the dynamic characteristics of the FG thick sandwich cylindrical shell are studied in various points across the thickness of cylinder. The analytical presented method provides an appropriate field for analysis of transient radial and hoop stresses in a cylinder on various thermo mechanical load. Accuracy of gained equations is evaluated by similar articles. The results have a good agreement with published data in pervious researches.

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In this paper, an analytical method is presented to study thermo-elastic behavior of nanoscale spherical shell subjected to thermal shock based on nonlocal elasticity theory. The shell is considered as elastic, homogeneous and isotropic solid. The nonlocal differential equation of motion is derived in terms of radial displacement. The analytical solution of equation of motion is obtained by Laplace transform and differential transform method (DTM). Mechanical boundary conditions are used to obtain unknown parameters that get in recurrence equation in Laplace domain. The results in Laplace domain is transferred to time domain by employing the fast inverse Laplace transform method (FLIT). Accuracy of obtained results is evaluated by well-known similar articles. The results have a good agreement in comparison with published data in pervious literatures. Also, the effects of nonlocal parameter and wall thickness of shell on the dynamic characteristics of nanoscale spherical shell are studied in various points across the thickness of shell under thermal shock. The present analytical method provides an appropriate field for analysis of times histories of radial and hoop stresses in a nanoscale shells subjected to various time dependent thermo-mechanical loads.

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In this paper, the stress intensity factor for an internal circumferential crack in a thick-walled cylinder has been determined. The cylinder has been subjected to an axisymmetric thermal shock on the outer surface according to the dual phase lag theory. The uncoupled, quasi-stationary thermoelastic governing equations have been assumed. The temperature and stress fields have been solved analytically in the Laplace domain and its Laplace inversion transform has been obtained numerically. Using weight function method, the stress intensity factor for mode-I has been extracted. Temperature, stress and stress intensity factor of hyperbolic and dual phase lag theories have been compared and the effects of heat flux and temperature gradient time relaxations on the temperature, stress and stress intensity factor have been studied. According to the results, the dual phase lag temperature distribution is different in comparison with the Fourier model. Also, the stress intensity factor for dual phase lag model is significant larger than Fourier one. Moreover, the maximum stress intensity factor in dual phase lag model occurs for a crack that the peak of stress wave reaches to its tip. Results show assumption of adequate heat conduction model for structure design under transient thermal loading is critical.