Random field finite elements

Wing Kam Liu*, Ted Belytschko, A. Mani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

538 Scopus citations


The probabilistic finite element method (PFEM) is formulated for linear and non‐linear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second‐moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in non‐linear continua. The accuracy and efficiency of the method is demonstrated by application to a one‐dimensional, elastic/plastic wave propagation problem and a two‐dimensional plane‐stress beam bending problem. The moments calculated compare favourably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

Original languageEnglish (US)
Pages (from-to)1831-1845
Number of pages15
JournalInternational Journal for Numerical Methods in Engineering
Issue number10
StatePublished - Oct 1986

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


Dive into the research topics of 'Random field finite elements'. Together they form a unique fingerprint.

Cite this