There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This study analyses the two-dimensional thermo-elastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical pressure vessels, by applying the third-order shear deformation theory (TSDT). The effective properties of FG-CNTRC cylindrical pressure vessels are computed for different patterns of reinforcement, according to the rule of mixture. The governing equations of the problem are derived from the principle of virtual works and are solved as a classical eigenproblem under the assumption of clamped supported boundary conditions. A large parametric investigation aims at showing the influence of some meaningful parameters on the thermo-elastic response, such as the type of pattern, the volume fraction of CNTs, and the Pasternak coefficients related to the elastic foundation.

https://www.mdpi.com/2079-4991/9/1/79/pdf

Higher-Order Thermo-Elastic Analysis of FG-CNTRC Cylindrical Vessels Surrounded by a Pasternak Foundation.

This article presents two-dimensional thermoelastic analysis of a functionally graded cylindrical pressure vessel subjected to axially variable thermal and mechanical loads. Thermal and mechanical properties are assumed to be variable along the radius based on the power law variation. Two-dimensional heat transfer equation along the axial and radial directions is analytically solved before thermoelastic analysis of the problem. First-order shear deformation theory is used for description of displacement field. Energy method as well as Euler equation is used to obtain final constitutive differential equations of the system. Four differential equations of the system are solved using the eigenvalue and eigenvector method for various patterns of axially variable loadings. Axial and radial distributions of displacement, strain, and stress components are calculated in terms of different parameters such as variable thermal and mechanical loadings and nonhomogeneous index. The obtained results indicate th...

The effect of axially variable thermal and mechanical loads on the 2D thermoelastic response of FG cylindrical shell

Analysis of graphene nanoplatelet reinforced cylindrical shell subjected to thermo-mechanical loads

This paper studies a nonlinear primary resonance of spiral stiffened functionally graded (SSFG) cylindrical shell with viscos damping force. The cylindrical shell is subjected to the harmonic excitation. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. The FG cylindrical shell with internal and external spiral stiffeners is investigated. The strain-displacement relations are obtained based on the von Karman nonlinear equations and the classical plate theory of shells. The smeared stiffener technique is used to model the under-studied SSFG cylindrical shell. The obtained partial differential equations of motion are discretized by means of the Galerkin method. In order to find the nonlinear primary resonance, the multiple scales method is adopted. The effects of various geometrical characteristics and material parameters on the nonlinear primary resonance response of spiral stiffened simply supported FG cylindrical shells are investigated.

Nonlinear primary resonance of spiral stiffened functionally graded cylindrical shells with damping force using the method of multiple scales

Two-dimensional thermoelastic analysis of functionally graded thick-walled cylinder is investigated under thermal and mechanical loadings and based on the Pasternak foundation. The first-order shear deformation theory is used to describe the displacement field. Fundamental governing differential equations of system are obtained by energy method and Euler equations. Effect of gradation of material properties and Pasternak foundation parameters are considered as important results of this study. The obtained results indicate that the end supports have considerable effect on the longitudinal distribution of components. Furthermore, it can be concluded that with increasing the non-homogeneous index, both radial and axial displacements decreases.

Two-dimensional thermoelastic analysis of FG cylindrical shell resting on the Pasternak foundation subjected to mechanical and thermal loads based on FSDT formulation

A. R. Abbasi

Papers

Two-dimensional thermoelastic analysis of FG cylindrical shell resting on the Pasternak foundation subjected to mechanical and thermal loads based on FSDT formulation