Stochastic Analysis of Heat Conduction and Thermal Stress Problems in a Nonhomogeneous Plate with Random Thermal Conductivity

Abstract

Stochastic temperature field in a nonhomogeneous plate with random thermal conductivity is analysed based on the Laplace transform and the perturbation method. The nonhomogeneous plate has the exponential variations in the thermal and mechanical properties in the direction of the thickness. The randomness of the thermal conductivity is considered to be a distribution function with random amplitude in the plate. Analytical expressions of the expected value and the variance for temperature and thermal stress are derived under the deterministic surface temperatures. Numerical calculations are carried out for the case that random variation in the thermal conductivity is a uniform distribution.