A structural reliability based method for identifying critical locations




Domyancic, Laura C.

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System reliability calculation for large-scale structural systems is complex due to the large number of potential failure locations and failure modes unless a priori knowledge can be used to significantly reduce the number of failure locations and modes. However, a priori knowledge may not be available for future aircraft systems that operate in new environments---such as hypersonic---or consist of unconventional designs with limited production runs. To address this issue, a fast filtering algorithm based on first order reliability methods (FORM) has been developed to numerically quantify the error incurred by filtering a limit state. A "filtering error" is calculated based on a certain limit state's contribution to the system probability of failure. This is compared to a chosen error tolerance to determine if a limit state is critical to the structural reliability or should be filtered.

Three hierarchical levels for finding the FORM solutions of the system limit states are presented. The first level is fast and scalable to large models and provides closed-form FORM solutions. Higher levels provide more accurate solutions with added computational expense. In this way, the problem of a very large system can be reduced by orders of magnitude by the initial filtering to only its critical locations. These locations can then be analyzed in detail at one of the higher level methods.

Numerous examples show the accuracy, efficiency, and limitations of the new algorithm. In most examples, Monte Carlo sampling was used to verify the critical locations. In all cases the filtering algorithm identified the same critical locations when sampling was performed on the linear limit states. The method is therefore most useful for problems with small probabilities of failure where sampling becomes computationally prohibitive. The method is tied to the limitations of FORM and may be unsuitable for highly non-linear problems.



First Order Reliability Method, Structural Reliability



Mechanical Engineering