Spatial orientation and topology optimization of modular trusses

Modularity in structural engineering offers significant cost advantages since identical components can be mass-produced in high quality-controlled facilities. While prior research has investigated the optimization of modular structures, this work is limited to the module topology periodicity, leading to solutions where some structure parts remain inefficiently used. This paper proposes a continuum-based formulation for optimizing simultaneously the module topology and spatial orientation in modular trusses. The numerical difficulties associated with the module rotations in the optimization formulation are identified, and properly handled by a novel topology-based rotation representation using group theory. A relaxation strategy based on complementary constraints enables the continuous integration of the module rotations in a lower-bound plastic design formulation (or fully stressed design). Case studies involving high density ground structures demonstrate that it is able in the worst case to retrieve the results obtained by imposing the module orientation a priori, and to improve the optimized design when freedom on the rotations is considered.