Thermal stress analysis of one- and two-dimensional functionally graded plates subjected to in-plane heat fluxes

Abstract

This study addresses the thermal stress analysis of one- and two-dimensional functionally graded plates subjected to in-plane heat fluxes. The material composition variation is assumed in-plane, not through the plate thickness according to a power-law distribution in terms of the volume fraction of the constituents. The mathematical model considers the spatial derivatives of local mechanical and thermal properties. The heat transfer and Navier equations of the two-dimensional thermo-elastic model were discretized using the finite difference method, and the set of linear equations were solved using the pseudo singular value method. The performance of both one- and two-dimensional functionally gradient material plates was investigated under two types of in-plane fluxes: one-edge and two-edges. For each type of heat fluxes, one- and two-dimensional functionally gradient material plates exhibited different displacement, stress and strain distributions. The temperature levels and distributions were affected with increasing ceramic constituent in the composition variation of the plate. One-dimensional functionally gradient material plate was more suitable for an one-edge heat flux along the direction of material composition variation, whereas two-dimensional functionally gradient material plate was more effective on the relieving the thermal stresses for a two-edges heat flux.

Finite-difference analysis of stresses of a non-uniform functionally graded material circular disk rotating in the magneto-thermal environment: An equal mass study

“…Central difference formulae are adopted for position derivative and backward difference formulae are implemented for time derivative. To evaluate the temperature fields, the equal number of nodal points with the equal mesh size are considered like equation (6). So, the size of each mesh is, Δr = (b−a)/(N-1).…”

“…Analysis of various structural components of functionally graded materials is quite extensive in literature. 1–10…”

“…Analysis of various structural components of functionally graded materials is quite extensive in literature. [1][2][3][4][5][6][7][8][9][10] The ample use of circular disks in engineering structures inspired researchers to analyze FGM circular disks under different loading conditions. Recently, so many works relating to the stress analysis of FGM circular disks under thermal, magneto-thermal, hygrothermal, etc.…”

A Review on Buckling Analysis of Functionally Graded Plates Under Thermo-Mechanical Loads

“…The first aspect in this part is the dimensionality of FGP, which refers to the number of dimensions through which properties variation occurs. Composition variation happens through the thickness, or the in-plane two dimensions [51,52] as shown in Fig. 3.…”

Effect of magnetic field on the thermo-elastic response of a rotating FGM Circular disk with non-uniform thickness

“…Generally, in FGM structures ceramics material is used with another material to withstand high temperature, corrosion, wear, and adverse environmental effect while maintaining their structural integrity. A number of studies have shown the viability of FGM structures in multiphysics problems involving beam, 10 plate, [11][12][13][14] shell, 15 pressure vessels. 16 In recent years, many studies have been conducted on the thermo-elastic field and magneto-thermo-elastic fields of circular disk which have extensively been used in many engineering components including grinding wheel, circular saw, high-speed gears, flywheel, gas turbine rotor, etc.…”