Stochastic Analysis of Thermoelastic Problems in a Nonhomogeneous Plate with Random Material Properties
Yoshihiro SUGANO, Ryoichi Chiba, Toshihiro KANNO · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A · 2006
A stochastic temperature solution is derived for the heat conduction problem in a nonhomogeneous plate with random thermal conductivity by perturbation method and Laplace transform. The nonhomogeneous plate, which has exponential variations in the thermal conductivity and mechanical properties through the plate thickness, is heated by a prescribed deterministic temperature on the one surface. The stochastic thermal stress problem in the nonhomogeneous plate with the random thermal conductivity or random coefficient of linear thermal expansion is analyzed thorough the use of thermal stress expression reported by one of present authors. Numerical results for the standard deviation of thermal stress are presented for the case that the randomness in the thermal conductivity and coefficient of linear thermal expansion is assumed to follow a uniform probability distribution.