Risk assessment through probabilistic structural analysis

Abstract

The increase in computer power over the last twenty to thirty years has resulted in the availability of a wide range of programs for structural analysis. Best-known among these are finite element programs which can solve many problems involving static and dynamic loading, heat transfer and fluid dynamics. Most of these programs are deterministic in that users specify “constant” values for the model parameters. In many instances this is sufficient: in the design or analysis of non-critical components, or ones for which all parameters are well-known, a deterministic analysis can provide adequate solutions. In the design of critical components the conventional approach is to perform a deterministic analysis and to build in reliability through suitably chosen safety factors. In problems where the risk associated with a component needs to be assessed conventional deterministic analysis methods are insufficient and methods which incorporate the probabilistic aspects of loads and material properties need to be used, especially if material degradation with time is a factor. Although the randomness of the problem parameters can be simulated through, for instance, Monte Carlo methods, these methods are computationally expensive. This paper discusses computationally efficient, fast probability integration methods where conventional deterministic programs can be adapted to calculate the reliability of a component using mean value-based perturbation methods. This adaptation has been performed for the general purpose finite element program ABAQUS and the general purpose fracture mechanics program NASCRAC. The methods are illustrated in a case study involving the fracture mechanics analysis of a turbine shaft: it is suspected that cracks have been present since commissioning at a shoulder in the shaft. The likely failure time and the probability of catastrophic failure prior to the first scheduled shutdown is calculated.