Basis random variables in finite element analysis

Galerkin's method is applied to random operator equations. Appropriate Hilbert spaces are defined for random functions and solutions are projected into these spaces, allowing the first‐ and second‐moment properties of the solution to be calculated. An equivalent energy‐based approach similar to the Rayleigh–Ritz method is developed, from which a stochastic finite element technique is derived. Several one‐ and two‐dimensional example problems are solved and the results discussed.