# An integrated design methodology for modular trusses including dynamic grouping, module spatial orientation, and topology optimization

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## Abstract

Modularity, a design philosophy in which a structure is comprised of identical components called modules, offers economical advantages as the modules can be mass produced in high quality controlled facilities. Prior research investigated structural optimization as a means of improving modular design, focusing on optimizing separately (i) the module topology and the module spatial orientation or (ii) the dynamic grouping into families of different topologies. This research did not include stability despite its considerable importance during preliminary design. In this paper, a novel integrated strategy is proposed for the preliminary design of modular trusses, unifying module topology, spatial orientation, and grouping optimization, as well as stability considerations to define meaningful solutions for real-life case studies. This is addressed by formulating an appropriate mixed-variable minimum volume problem in elastic design, including multiple load cases with self-weight and stress limitations in tension and compression. Global stability is considered through a linear prebuckling constraint, and a local buckling constraint is formulated by considering Euler buckling with standard profiles obtained from commercial catalogues. The practical applicability of this contribution is demonstrated on a benchmark modular bridge and a three-dimensional modular vault structure. The importance of stability considerations is also investigated, where the redundancy introduced by modularity is shown to contribute to the global resistance of the entire structure.

## Keywords

Modular trusses Truss topology optimization Simulated annealing Mixed-variable optimization problem## Notes

### Funding information

This study is finacially supported by the Fond National de la Recherche Scientifique (F.R.S-FNRS, Belgium).

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