In the early phase of structural design, uncertainties arise from many sources of variations. Therefore, the manner in which the uncertainties in the design phase are handled is of great importance. Designers need to figure out an outline of the topological structure and have to compare the evaluation results of diverse design ideas from multiple aspects under some uncertain design information at the design phase. We have proposed a preference set-based design (PSD) method that generates a ranged set of design solutions that satisfy sets of performance requirements under various sources of uncertainties, while capturing a designer's preference. This study proposes a design method for the early phase of structural design that is possible to obtain the multi-objective satisfactory solution with topological and geometrical uncertainty and variability by applying the PSD method to the finite element method. This study discusses the suitability of our proposed approach for obtaining the multi-objective satisfactory solution sets by applying to the design problems of a cantilever with uncertainties of design parameters which define the topology of the structure.
