Abstract
The statistics of the temperature and thermal stress are derived analytically in functionally graded material plates (FGM plates) with randomly varying initial temperature and arbitrary nonhomogeneous thermal and mechanical properties through the thickness of plate. The transient temperature field is analyzed based on a kind of integral transform developed by Vodicka, which is obtained by approximating the FGM plates as multilayered plates with distinct thermal constants in each layer. The associated transient thermal stress is obtained by using the closed-form solution derived by one of the authors for a nonhomogeneous plate with arbitrary variations in mechanical properties. The analytical expressions of autocorrelation function and power spectral density for the temperature and thermal stress are derived. Numerical calculations are carried out, assuming that the random initial temperature of the FGM plates is a white noise disturbance or a homogeneous Markov random field. The effects of the gradual change in material composition on the statistics of temperature and thermal stress for the two homogeneous random fields are discussed.
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