Interval analysis framework for structural safety assessment

Abstract

Uncertainties inherently exist in structural parameters and loading regimes. The inevitable impact of uncertainties deteriorates actual performance of engineering structures, which consequently compromises the structural safety. Failure in appropriately assessing the effect of uncertainties on structural safety would cause tragic yet irreversible consequences. Therefore, the continuous demand of reliable uncertainty analysis and robust safety assessment has stimulated the study of this thesis.

The dissertation presents a series of novel numerical methods using mathematical programming approaches to perform safety assessment for engineering structures involving non-random uncertain parameters. Particularly, five robust uncertainty analyses have been developed. Firstly, uncertain linear static analysis of discrete structures based on finite element analysis is investigated. Uncertain linear bifurcation buckling analysis with interval parameters is then solved to determine the extreme cases of structural safety. Interval limit analysis of ductile engineering structures with rigid perfectly plastic material is carried out to evaluate the extreme structural collapse strength. The scope of the uncertain limit analysis is further extended to incorporate Info-gap uncertainty model. Finally, the fuzzy limit analysis is conducted to efficiently achieve the extreme fuzzy profile of the collapse load limit. Numbers of representative numerical examples have been elaborately selected to illustrate the accuracy, efficiency, as well as the applicability of these uniquely developed uncertainty analyses.

The developed uncertainty analysis schemes are capable of providing the extreme circumstances of structural outputs with higher quality of sharpness and efficiency regardless of large extent of uncertainties. The proposed schemes are capable of offering the information on the critical values of uncertain parameters causing the extreme situations at zero computational cost. This adjunct ability supplies beneficial information to engineers which become very useful in engineering designs. Furthermore, the extensive applicability, as one of the major requirements, has been consistently preserved throughout each developed uncertainty analysis. Since the proposed schemes are computationally orientated approaches, the potential integration with modern engineering software is simple. Engineers can implement these schemes directly into real-life engineering applications without requirements of substantial background knowledge of developments of these numerical schemes.