In this paper, the thermopiezoelectric behavior of a thick walled cylinder with functionally graded materials is studied. The cylinder is loaded under the temperature gradient and inner and outer pressures. All the mechanical, thermal and piezoelectric properties except the Poisson ratio can be expressed as a power function in the radial direction. In the first step, with the solution of the heat transfer equation, a symmetric distribution of temperature is obtained. The stresses and electric displacement relations can be derived in terms of the temperature, electric field and strain. Substituting the resultant relations into the mechanical and electrical equilibrium equations yields the system of nonhomogeneous differential equations with two unknown variables (the mechanical displacement and the electrical potential). Solving the system of nonhomogeneous differential equations yields other mechanical and thermal terms such as the stress, displacement, electric field and electric displacement. The main result of the present study is that, by applying a proper distribution of mechanical and thermal properties in the functionally graded piezoelectric material (FGPM) solid structures, the distributions of stresses, electric potential and electric field in the FGPM can be controlled. Hence, the FGPM can be used in sensors or actuators.

In this paper, the buckling analysis of laminated composite plates reinforced by single-walled carbon nanotubes (SWCNTs) is carried out using an analytical approach as well as the finite element method. The developed model is based on the classical laminated plate theory (CLPT) and the third-order shear deformation theory for moderately thick laminated plates. The critical buckling loads for the symmetrical layup are determined for different support edges. The Mori-Tanaka method is employed to calculate the effective elastic modulus of composites having aligned oriented straight nanotubes. The effect of the agglomeration of the randomly oriented straight nanotubes on the critical buckling load is also analyzed. The results of analytical solution are compared and verified with the FEM calculations The critical buckling loads obtained by the finite element and the analytical methods for different layup and boundary conditions are in good agreement with each other. In this article, the effects of the carbon nanotubes (CNTs) orientation angle, the edge conditions, and the aspect ratio on the critical buckling load are also demonstrated using both the analytical and finite element methods.

In this paper, free and forced vibration analysis of multi-layered functionally graded composite cylindrical panels reinforced by single wall carbon nanotubes is presented. The panel is composed of different layers which are reinforced using carbon nanotubes arranged in arbitrary directions. Reddy’s third-order shear deformation theory is used which makes results more accurate especially for thick panels. The set of governing equations and boundary conditions is derived using Hamilton’s principle and is solved numerically using generalized differential quadrature method and Newmark beta method. Convergence and accuracy of the presented solution are confirmed and effect of volume fraction, distribution and orientation of carbon nanotubes and geometrical parameters on the natural frequencies of the panel are investigated for different boundary conditions. Also, effect of volume fraction and orientation of carbon nanotubes on the dynamic response of the panel are investigated. Result of this paper can be considered as a useful tool in dynamic analysis of multilayer carbon nanotube-reinforced structures.

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The small-scale effect on the torsional buckling of a double-walled carbon nanotube (DWCNT) embedded on Winkler and Pasternak foundations is investigated in this study using the theory of nonlocal elasticity. The effects of the surrounding elastic medium, such as the spring constant of the Winkler type and the shear constant of the Pasternak type, as well as the van der Waals (vdW) forces between the inner and the outer nanotubes are taken into account. Finally, based on the theory of nonlocal elasticity and by employing the continuum models, an elastic double-shell model is presented for the nonlocal torsional buckling load of a DWCNT. It is seen from the results that the shear constant of the Pasternak type increases the nonlocal critical torsional buckling load, while the difference between the presence and the absence of the shear constant of the Pasternak type becomes large. It is shown that the nonlocal critical buckling load is lower than the local critical buckling load. Moreover, a simplified analysis is carried out to estimate the nonlocal critical torque for the torsional buckling of a DWCNT.

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