Transient probabilistic systems

Wing Kam Liu*, Glen Besterfield, Ted Belytschko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

86 Scopus citations


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 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 a linear continuum problem and potential applications to nonlinear problems are discussed.

Original languageEnglish (US)
Pages (from-to)27-54
Number of pages28
JournalComputer Methods in Applied Mechanics and Engineering
Issue number1
StatePublished - Mar 1988

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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