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 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 undesirable secular terms. A method based on Fourier analysis is presented for removing secularities from the PFEM. The effectiveness of the Lanczos reduction technique and the secularity elimination scheme is demonstrated with application to the linear continuum problem and potential applications to nonlinear problems are discussed.
scientific article; zbMATH DE number 4005763
scientific article