Abstract: The formulation of deterministic optimization in no way takes into account
the randomness of the design variables [Chybiński, M., Garstecki, A. (2017), Czubacki, R.,
Lewiński T. (2020)]. Optimum structures are particularly sensitive to parameter imperfections.
Optimal solutions located on the border of the acceptable area may relatively easily turn out
to be completely useless if the parameter values differ from the assumed nominal values. It
seems natural to extend the formulation of deterministic optimization, which takes into
account the uncertainty of parameter values. Robust optimization proposed in the paper
offers such possibilities. In the paper, robust optimisation is discussed on the example of
a single-layer lattice covering. After dimensioning the individual groups of bars, the safety
level of the structure was assessed by determining the reliability index and failure probability.
The structure under analysis is susceptible to stability failure resulting from the condition of
the node snap-through. On this basis, a displacement limit function was adopted, which refers
to the maximum displacement value at the instant of the node snap-through. Next, two
methods of structure optimisation (deterministic and robust), based on analogous constraints
and objective function, were compared. The comparison of both methods ends with
a reassessment of the safety level of the structure. As a result of robust optimization,
a structure with a slightly larger mass was obtained. The difference in the weight of the structure
in the case of deterministic and immunity optimization did not exceed 2%. However, the
reliability index, which measures the safety of the structure, has increased significantly. At the
expense of a slight increase in weight, we obtained a structure that is more reliable and resistant
to the dispersion of parameters characterizing the structure’s operation.
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