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Research Directions in Computational Mechanics (1991) / Chapter Skim
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9 Uncertainty and Stochastic Processes in Mechanics
Pages 94-98

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From page 94...
... Reliability analysis applications to enhance public safety include the performance of structures when subjected to seismic loads, determination of inspection cycles for aging aircraft, and evaluation of existing infrastructure such as bridges and lifelines. In the design of mechanical components and systems where safety is not a crucial issue, reliability engineering is also important because it can provide cost-ef fective methods for enhanced fabrication and inspection.
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From page 95...
... Pa = D( - m dn (9~1) In current engineering practice the reliability of a structure against excessive crack growth is usually ascertained by performing linear stress analysis and then using S- n charts, which provide the engineer with the probability of failure due to fatigue fracture of a component subjected to n cycles to a maximum stress S
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From page 96...
... Some of the current models are able to reflect the randomness in the seismic source mechanism, propagation path, and surface layer soil amplification. The difference in ground motion and resulting structural response estimates arising from the use of various models represents modeling as well as parametric uncertainties, since each component model contains a certain number of parameters to which appropriate values must be assigned for numerical analysis.
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From page 97...
... The stochastic variability of these parameters is idealized in terms of stochastic f ields, multivariate and multidimensional as appropriate, for continuous systems and by means of a multivariate random variable for discretized systems. The resurgence of interest appears to have arrived at a time when the finite element method has finally reached its maturity, so that the finite element solution to the problem of system stochasticity can augment existing software packages and thus provide added value.
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From page 98...
... BOUNDING TECHNIQUES The primary difficulty associated with probabilistic models dealing with intrinsic randomness and other sources of uncertainty often lies in the fact that a number, for that matter usually a large number, of assumptions must be made in relation to the random variables and/or stochastic processes that analytically idealize the behavior of mechanical and structural systems. In this regard the following statement is in order: When uncertainty problems cloud the process of estimating the structural response, the use of bounding techniques permits estimation of the maximum response, which depends on only one or two key parameters of design and analysis.
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Key Terms

  • computational mechanics
  • response function
  • finite element
  • structural response
  • paris law

  • variability response
  • stochastic variability
  • mechanical components
  • response variability
  • stochastic properties

  • random variable
  • stochastic finite
  • maximum response
  • reliability engineering
  • bounding techniques

  • neuman expansion
  • ground motion
  • behavior crack
  • random variables
  • estimated provides

  • ground accelerations
  • improved computational
  • squared multiplied
  • simulation techniques
  • constitutive behavior

  • vibration analysis
  • techniques permits
  • random vibration
  • recent effort
  • finally reached


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