Thermoelastic Analysis of Rotating Functionally Graded Truncated Conical Shell by the Methods of Polynomial Based Differential Quadrature and Fourier Expansion-Based Differential Quadrature

Aref Mehditabar,Kerameat Malekzadeh Fard,Gholam H Rahimi

doi:10.1155/2018/2804123

Abstract

This paper focuses on the three-dimensional (3D) asymmetric problem of functionally graded (FG) truncated conical shell subjected to thermal field and inertia force due to the rotating part. The FG properties are assumed to be varied along the thickness according to power law distribution, whereas Poisson’s ratio is assumed to be constant. On the basis of 3D Green-Lagrange theory in general curvilinear coordinate, the fundamental equations are formulated and then two versions of differential quadrature method (DQM) including polynomial based differential quadrature (PDQ) and Fourier expansion-based differential quadrature (FDQ) are applied to discretize the resulting differential equations. The reliability of the present approach is validated by comparing with known literature where good agreement is reached using considerably few grid points. The effects of different mechanical boundary conditions, temperature fields, rotating angular speed, and shell thickness on the distributions of stress components and displacement in thickness direction for both axisymmetric and asymmetric cases are graphically depicted.

Highlights

Sharp discontinuity and delamination problems in monolithic laminated composite materials impelled scientists to come up with the idea of new class of advanced composite material, so-called functionally graded materials (FGMs)
This paper focuses on the three-dimensional (3D) asymmetric problem of functionally graded (FG) truncated conical shell subjected to thermal field and inertia force due to the rotating part
FGMs are characterized by smooth variations in material properties from one interface to other based on specific function

Summary

Introduction

Sharp discontinuity and delamination problems in monolithic laminated composite materials impelled scientists to come up with the idea of new class of advanced composite material, so-called functionally graded materials (FGMs). Xin et al [13] discussed the thermoelastic responses of the thick-walled FG tube under thermal and mechanical load fields employing Voigt method. Kordkheili and livani [16] proposed a semianalytical-numerical method to investigate the thermoelastic responses of the FG rotating disks with variable thickness and in another work the thermoelastic analysis coupled with creep behavior [16] of the same problem was carried out by them. Jabbari et al [19] investigated the thermoelastic problem of the rotating thick FG cylindrical shell with material gradient in axial direction utilizing multilayer method (MLM). In this paper 3D asymmetric thermoelastic analysis of rotating FG truncated conical shell under temperature gradient through thickness and centrifugal load duo to rotation of the shell is investigated. The sensitivities of displacement and stress components to different values of thermal loading, thickness of shell, rotating angular speed, and boundary conditions under both axisymmetric and asymmetric loading conditions are graphically plotted and discussed

Governing Equations

The Method of Solution

Numerical Results and Discussion

Conclusion