Kuhn-Tucker optimization based reliability analysis for probabilistic finite elements

Wing K Liu*, G. Besterfield, M. Lawrence, T. Belytschko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The fusion of the probabilistic finite element method (PFEM) and reliability analysis is presented. The application of the methodologies is directed toward probabilistic fracture mechanics (PFM). That is, for uncertainties in loads, material parameters, geometry and crack length, orientation and location, the probability of fracture is determined. In order to calculate the reliability index for determination of the probability of failure or fracture, a Kuhn-Tucker optimization procedure is used. Application of the Kuhn-Tucker optimization procedure provides a concise manner for performing reliability analysis. By employing an enriched finite element which embeds the crack-tip singularity, explicit expressions are developed for the PFEM and optimization procedure. The fusion of PFEM and reliability is computationally quite efficient and provides a powerful tool for the design engineer.

Original languageEnglish (US)
Pages (from-to)135-149
Number of pages15
JournalAmerican Society of Mechanical Engineers, Applied Mechanics Division, AMD
StatePublished - Dec 1 1988

ASJC Scopus subject areas

  • Mechanical Engineering


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