Stochastic Finite Elements with Multiple Random Non-Gaussian Properties

The spectral formulation of the stochastic finite-element method is applied to the problem of heat conduction in a random medium. Specifically, the conductivity of the medium, as well as its heat capacity are treated as uncorrelated random processes with spatial random fluctuations. Using the spectral stochastic finite-element method, this paper analyzes the sensitivity of heat conduction problems to probabilistic models of random data. In particular, both the thermal conductivity and the heat capacity of the medium are assumed to be uncertain. The implementation of the method is demonstrated for both Gaussian and lognormal material properties, modeled either as random variables or random processes.