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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 study, static and free vibration behaviors of two type of sandwich plates based on the three dimensional theory of elasticity are investigated. The core layer of one type is functionally graded (FG) with the homogeneous face sheets where as in second type the core layer is isotropic with the face sheets FG material. Plate is under uniform pressure at the top surface and free from traction in the bottom surface. The effective material properties of FG layers are estimated to vary continuously through the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. State space differential equations are obtained from equilibrium equations and constitutive relations. The obtained governing differential equations are solved by using Fourier series expansion along the in plane directions and state space technique across the thickness direction. Accuracy and exactness of the present approach is validated by comparing the numerical results with the published results. Furthermore it is possible to validate the exactness of the conventional two dimensional theories. Finally the influences of volume fraction, width-to-thickness ratios and aspect ratio on the vibration and static behaviors of plate are investigated.

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Conventional Ritz and Galerkin methods based on local theory of elasticity employ polynomials as their approximating functions, however these methods are not convenient to use in three-dimensional nonlocal analysis. In the present study, to conquer this difficulty, a type of weighted residual approach with a set of trigonometric approximating functions were developed. By using appropriate trigonometric approximating functions, it is possible to consider the effect of various edges boundary condition on frequency behavior of nanoplate. Validation of present formulation is carried out by comparing numerical result with the published results. It is concluded that the effect of nonlocal parameter on natural frequencies is significant especially in higher modes due to the lower wavelength of the mode. The research shows that in nonlocal elasticity there are distinct discrepancies between behaviors of two and three-dimensional results. In addition, the difference between the two- and three-dimensional results in local elasticity is not as noticeable as in nonlocal elasticity. Furthermore, the effects of length to thickness ratio, aspect ratio, nonlocal parameter and different boundary conditions on fundamental natural frequency of nanoplates were studied. This benchmark solution can be used to assess the accuracy of conventional two-dimensional theories.