Stochastic thermoelastic problem of a functionally graded plate under random temperature load

Abstract

This study attempts to derive the statistics of temperature and thermal stress in functionally graded material (FGM) plates exposed to random external temperatures. The thermomechanical properties of the FGM plates are assumed to vary arbitrarily only in the plate thickness direction. The external temperatures are expressed as random functions with respect to time. The transient temperature field in the FGM plate is determined by solving a nonhomogeneous heat conduction problem for a multilayered plate with linear nonhomogeneous thermal conductivity and different homogeneous heat capacity in each layer. The autocorrelations and power spectrum densities (PSDs) of temperature and thermal stress are derived analytically. These statistics for FGM plates composed of partially stabilised zirconia (PSZ) and austenitic stainless steel (SUS304) are computed under the condition that the fluctuation in the external temperature can be considered as white noise or a stationary Markov process.

Stochastic Analysis of Natural Convection in Vertical Channels with Random Wall Temperature

“…This divergence is also observed in the mean square temperature of solids when the boundary temperature is given by white noise [18,21,22]. A sharp increase in the slope of the mean square near the channel wall results from high-frequency components [22]. Figure 3 shows that the mean square velocity has bellshaped profiles (convex upward), and it exhibits peak values in the vicinity of = 0.6.…”

“…The divergence of the mean square on the heated channel wall (i.e., = 1) is attributed to the white noise's feature of having an infinite variance. This divergence is also observed in the mean square temperature of solids when the boundary temperature is given by white noise [18,21,22]. A sharp increase in the slope of the mean square near the channel wall results from high-frequency components [22].…”

Stochastic analysis of a thermoelastic problem in functionally graded plates with uncertain material properties

“…B i (i = 1, 2, 3) are positive constants depending on the correlation strengths, whereas C 1 is a constant whose value ranges from −1 to 1. Equations (4)- (6) express the autocorrelation of the thermal conductivity, the autocorrelation of the CTE and the cross-correlation between the thermal conductivity and CTE, respectively.…”

“…Madera [13] developed a numerical method for the determination of nonstationary stochastic three-dimensional temperature fields for nonhomogeneous bodies of an arbitrary shape with arbitrary stochastic boundary conditions. Sugano et al analysed the stochastic thermal stress in FGM plates subjected to random surface temperatures [25,26] and random surrounding medium temperatures [6]. Sugano et al [24] also analysed the stochastic thermal stress in an FGM plate with a random distribution of initial temperature.…”

Stochastic Analysis of Heat Conduction and Thermal Stresses in Solids: A Review

“…Figure 2. Effects of location-dependent thermal conductivity on mean square temperature [39] Chiba et al [41] addressed the stochastic thermal stress problem of functionally graded plates convectively heated from the surrounding medium whose temperature fluctuates randomly. The material properties of the plates are allowed to vary arbitrarily along the thickness direction.…”