TRANSIENT PROBABILISTIC SYSTEMS

The probabilistic finite element method (PFEM) for the transient analysis of random field problems by the finite element method is presented with improved computational procedures. The theoretical development of PFEM is reviewed with the inclusion of a transformed uncorrelated random variable, the formulation of the decoupled PFEM equations, and the computations of the probabilistic distributions. A method is presented to reduce the PFEM equations to a smaller system of tridiagonal equations. The reduction scheme is based on a highly efficient Lanczos algorithm which forms a reduced basis from the system eigenproblem. The application of PFEM via a sensitivity method for transient problems can result in the emergence of undersirable secular terms. This work is pertinent to structural problems.