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Thermomechanical responses of functionally graded cylinders

Eker Mehmet, Yarımpabuç Durmuş

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 4

19--28

EN

In this study, thermal and mechanical stresses in hollow thick-walled functionally graded (FG) cylinders is presented under the convection boundary condition. The convective external condition and constant internal temperature in hollow cylinders are investigated. Inhomogeneous material properties produce irregular and two-point linear boundary value problems that are solved numerically by the pseudospectral Chebyshev method. The displacement and thermal stress distributions are examined for two different material couples under particular boundary conditions that are similar to their real engineering applications.Results have demonstrated that the pseudospectral Chebyshev method has low computation costs, high accuracy and ease of implementation and can be easily customized to such engineering problems.

2

An analytical investigation of a 2D-PPMs hollow infinite cylinder under thermo-electro-mechanical (TEM) loadings

Meshkini M., Firoozbakhsh K., Jabbari M., SelkGhafari A.

Journal of Theoretical and Applied Mechanics

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2018

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Vol. 56 nr 1

107--122

EN

The analytical solution of steady-state asymmetric thermo-electro-mechanical loads of a hollow thick infinite cylinder made of porous piezoelectric materials (2D-PPMs) based on two-dimensional equations of thermoelasticity is considered. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to solve the heat conduction equation and the non-homogenous system of partial differential Navier equations using the complex Fourier series and the powerexponential law functions method. The material properties are assumed to depend on the radial and circumferential variable and are expressed as power-exponential law functions along the radial and circumferential direction.

3

Equilibrium and stability of nonlinearly elastic cylinder made of Blatz-Ko material

Obrezkov L.

Engineering Transactions

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2016

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Vol. 64, iss. 4

457--463

EN

The Blatz-Ko model describing the behavior of nonlinearly elastic compressible material was used to model the process of stretching and inflation of hollow cylinder, both thick- and thin-walled. By means of semi-inverse method, the three-dimensional problem was reduced to the analysis of boundary-value problem for ordinary differential equation of second order. The presented numerically constructed loading diagrams show in this the model that even the regions of positive stresses can contain zones of instability. Within the framework of bifurcation analysis, size of these zones and their dependence on material parameters were determined.

4

Axisymmetric steady temperature field in FGM cylindrical shells with temperature-dependent heat conductivity and arbitrary linear boundary conditions

Moosaie A.

Archives of Mechanics

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2015

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Vol. 67, nr 3

233--251

EN

An approximate analytical solution to the axisymmetric heat conduction equation for a hollow cylinder made of functionally graded material with temperature-dependent heat conductivity is presented. General linear boundary conditions are considered. The Poincaré method for regular perturbation problems is employed to obtain an analytical closed-form approximate solution for the temperature field. The hierarchical asymptotic problems are solved up to the second-order approximation. A numerical example is worked out, i.e., the one-dimensional heat conduction in the radial direction with prescribed temperatures at the boundaries. The approximate temperature profiles are compared with a numerical solution of the full nonlinear problem which provides the reference “exact” solution. A good agreement between the approximate and reference solutions is established. The convergence of the asymptotic series as well as the properties of the temperature field are studied.

5

Phase velocity and attenuation of longitudinal shear vibrations of hollow poroelastic cylinders

Ahmed Shah S., Javvad Hussaini S.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 2

337--346

EN

The present paper is devoted to the study of phase velocity and attenuation of longitudinal shear vibrations of hollow poroelastic circular cylinders in the presence of dissipation. The explicit expressions for phase velocity and attenuation of longitudinal shear vibrations are derived. The frequency equation of longitudinal shear vibrations and modes obtained in a previous paper are used to compute the phase velocity and attenuation for different dissipations for thin and thick poroelastic cylindrical shells and poroelastic solid cylinder. The physical parameters of sandstone saturated with kerosene and sandstone saturated with water are used for the purpose of computation. It is found that the phase velocity is linear beyond certain frequency. Phase velocity is smaller for a typical anti-symmetric mode compared to the flexural mode. It is greater for the second mode than that of the first mode. Also the phase velocity is larger for a thin poroelastic cylindrical shell than that of a thick poroelastic cylindrical shell. The same is true for attenuation also. Attenuation is very high for the considered dissipations and it increases with the increase in dissipation.