Finite element methods in probabilistic mechanics

Wing Kam Liu, A. Mani, Ted Belytschko

Research output: Contribution to journalArticlepeer-review

118 Scopus citations


Probabilistic methods, synthesizing the power of finite element methods with second-order perturbation techniques, are formulated for linear and nonlinear problems. Random material, geometric properties and loads can be incorporated in these methods, in terms of their fundamental statistics. By construction, these methods are applicable when the scale of randomness is not too large and when the probabilistic density functions have decaying tails. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. Applications showing the effects of combined random fields and cyclic loading/stress reversal are studied and compared with Monte Carlo simulation results.

Original languageEnglish (US)
Pages (from-to)201-213
Number of pages13
JournalProbabilistic Engineering Mechanics
Issue number4
StatePublished - Dec 1987

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Civil and Structural Engineering
  • Nuclear Energy and Engineering
  • Condensed Matter Physics
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering


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