Analytical solution of micropolar functionally graded materials (FGM) hollow cylinder under thermal asymmetric load (r, θ)

Abstract

This paper focuses on the analysis of two‐dimensional steady‐state thermal stresses based on micropolar theory in hollow and solid cylinders which are made of functionally graded materials (FGM) under asymmetric loading condition (r, θ) with the general thermal and mechanical boundary conditions along the inside and outside surfaces. The heat conduction and Navier equations were solved using the separation of variables and complex Fourier series for micropolar theory. Finally, the exact numerical results for both micropolar and classical solutions are illustrated and discussed using two examples: In Example 1, based on the micropolar theory, when thermal tensions are exerted on the inside surface of the cylinder, some of the strain energy is used for the object rotation; therefore, considering this condition, the calculated values resulted from the micropolar theory are smaller than those of the classic theory. In Example 2, by exerting normal tension on the inside surface of the cylinder, the rotation created is very small; therefore, the results of the micropolar and classic theories are similar. In addition to FGM materials, this solution is applicable to minerals and organic matter multiphase fiber and particulate composites, soil, rock, concrete, and various granular materials [59].

An investigation on the torsional vibration of a FG strain gradient nanotube

“…The two phase local/nonlocal deformation of thermo electrical reinforced composites was studied by Selvamani et al [70] with the Navier method. It is possible to see these methods used in the briefly mentioned articles and in other studies [28,29,49,53,[71][72][73][74][75][76][77] as well. In our study, Fourier sine series with Stokes' transform is considered for functionally graded porous nanotubes.…”