Stochastic finite element modelling in linear transient heat transfer

A stochastic heat transfer variational principle is suggested for transient and steady-state heat problems. The non-statistical formulation is based on the combination of the second-order perturbation technique and second-moment analysis. The principle allows incorporation of system uncertainties into the conventional finite element equations, which are solved for the first two probabilistic moments of the nodal random temperature held. Computational aspects of the problem are discussed. Numerical algorithms have been worked out and easily adapted to an existing finite element code. The formalism presented may be directly employed for a wide class of field problems.