Numerical strategies for structural robustness assessment

Abstract eng:
The robustness of a structure, understood as its ability not to suffer disproportionate damages as a result of a limited initial failure, is an intrinsic requirement, inherent to its static system. A robust design should therefore take into account the different responses to the damage that result from distinct organizations of the composing elements in the whole system and cannot be limited to design the structure for additional accidental load case. For this purpose a numerical evaluation of the robustness degree of a structure, defined as the decrement of structural quality corresponding to an increment of the damage level, is presented. The approach resorts a nonlinear analysis of the damaged structural configurations and takes the ultimate resistance as parameter for the structural performance and the number of failed elements as parameter for the damage level: this means that several configurations correspond to each damage level, since different combinations of the removed elements are possible. Among these combinations, the best and the worst configurations have to be identified for each damage level (i.e. the configurations that show the highest and the lowest response respectively). By diagramming the trend of these two values, two curves are obtained, that provide a lower and upper bound for the structural robustness of the structure. Problems arise from the fact, that the exhaustive number of combinations increases exponentially with the number of elements: in order to perform a feasible limited number of analyses for one structure, optimization algorithms have to be used with the aim of moving the problem complexity from an exponential to a polynomial form. In this paper a heuristic optimization is presented, which assumes that the worst and the best configuration for each damage level can be directly originated by an element removal on the best and worst configurations of the previous damage level, respectively. In this way, the problem complexity moves from an exponential to a polynomial form and becomes computationally feasible. The method is applied to some relatively simples structures and the role played by the static indeterminacy level and its distinguishing aspects (restraints, continuity level and element number) is particularly outlined. Some robustness indicators are also presented, that can be extrapolated from the obtained robustness curves and that describe the robust response of the structure.

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