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

Abstract

The statistics (i.e., mean and variance) of temperature and thermal stress are analytically obtained in functionally graded material (FGM) plates with uncertainties in the thermal conductivity and coefficient of linear thermal expansion. These FGM plates are assumed to have arbitrary nonhomogeneous thermal and mechanical properties through the entire thickness of plate and are subjected to deterministic convective heating. The stochastic temperature and thermal stress fields are analysed by assuming the FGM plate is multilayered with distinct, random thermal conductivity and coefficient of linear thermal expansion in each layer. Vodicka's method, which is a type of integral transform method, and a perturbation method are employed to obtain the analytical solutions for the statistics. The autocorrelation coefficients of each random property and cross-correlation coefficients between different random properties are expressed in exponential function forms as a non-homogeneous Markov random field of discrete space. Numerical calculations are performed for FGM plates composed of partially stabilised zirconia (PSZ) and austenitic stainless steel (SUS304), which have the largest dispersion of the random properties at the place where the volume fractions of the two constituent materials are both 0.5. The effects of the spatial change in material composition, thermal boundary condition and correlation coefficients on the standard deviations of the temperature and thermal stress are discussed.

Non-Axisymmetric Thermal Stress Around a Circular Hole in a Functionally Graded Infinite Plate

“…(1) and (7), Eqs. (16) and (17) can be rewritten as g j z + g j z = g j+1 z + g j+1 z (18) j g j z − j g j z = j+1 g j+1 z − j+1 g j+1 z…”

“…Lee et al [15] investigated the static responses of metal and ceramic functionally graded plates subjected to thermal and mechanical loads. Chiba and Sugano [16] analytically obtained the statistics of temperature and thermal stress in FGM plates with uncertainties in the thermal conductivity and coefficient of linear thermal expansion. Gunes and Reddy [17] carried out geometrically nonlinear analysis of functionally graded circular plates subjected to mechanical and thermal loads by using the Green-Lagrange strain tensor in its entirety.…”

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

“…The analysis of the results showed that deviations in the ceramic/metal volume fraction produce significant randomness in the thermal stress and safety factor distribution of the plate. Chiba et al [79,82] stochastically analyzed the transient heat conduction and thermal stress problems of infinite FGM plates with an uncertain thermal conductivity and coefficient of thermal expansion. The FGM plates were assumed to have arbitrary thermal and mechanical nonhomogeneities along the thickness direction.…”

“…The FGM plates were assumed to have arbitrary thermal and mechanical nonhomogeneities along the thickness direction. Two methods were used for the analysis: the direct Monte Carlo simulation method [79] and a perturbation method [82]. Sugano et al [81] analyzed the thermoelastic problem of nonhomogeneous plates with a random thermal conductivity and coefficient of thermal expansion.…”

A Non-Intrusive Stochastic Isogeometric Analysis of Functionally Graded Plates with Material Uncertainty

“…A stochastic perturbation technique was adopted to study the free vibration characteristics of FGM plates in [11,12]. The spectral stochastic isogeometric analysis (SSIGA) using the first order deformation theory was implemented by Keyen Li et al to obtain the static response of the FGM plates [13].…”