The design of structures using topology optimization can improve the structural performance and save material, in turn reducing costs. Using a framework of large-scale, three-dimensional topology optimization implemented by the authors in an open-source multiphysical software, we investigate the influence of uncertain loading on the optimized design. Direct differentiation is used to reveal the relationship between displacements and applied force, giving an efficient and effective tool to postprocess optimized topologies. The developed methodology for the assessment of the sensitivity with respect to applied forces is explored using two three-dimensional examples: the classic MBB cantilever and a cableway pylon. The advantages and limitations of this method are discussed.
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