Reliability methods for finite element models

Probabilistic techniques in engineering problems are needed because they provide a deeper understanding of failure mechanisms and occurrence probabilities than deterministic techniques. In addition, they draw our attention to the consequences of failure at an early stage in the design process. However, to achieve these advantages, a well-defined model of the structure together with a robust reliability technique is needed. On the other hand, complex engineering problems with complicated boundary conditions usually are analysed with the finite element technique as presented. The finite element method provides an implicit approximation to the limit state equation (LSE) that is far more accurate than other approaches. Therefore, if one wants to have the full advantage of the probabilistic approach one needs both an advanced model and a supporting reliability technique. Known reliability techniques can be classified in three levels according to their performance. For the reliability analysis of engineering structures a variety of methods is known, of which Monte Carlo simulation is widely considered to be among the most robust and most generally applicable. The absence of systematic errors and the fact that its error analysis is well-understood are properties that many competing methods lack. A drawback is the often large number of runs needed, particularly in complex models, where each run may entail a finite element analysis or other time consuming procedure. Variance reduction methods may be applied to reduce simulation cost. This study describes methods to reduce the simulation cost even further, while retaining the accuracy of Monte Carlo, by taking into account widely-present monotonicity in limit state equations or other prior information. This dissertation focuses on problems where a highly accurate estimate of the failure probability is required, but an explicit expression for the limit state equation is unavailable and the limit state equation can only be evaluated without loss of accuracy via finite element analysis or some other time consuming process