Customized topology optimization of tensegrity modules for modular assembly

Modular assembly has emerged as an effective strategy for the design of complex structures, while offering a promising framework for the development of tensegrity structures. However, efficiently identifying tensegrity modules suitable for modular assembly remains a significant challenge due to the diversity of assembly scenarios and design requirements. To address this issue, this study proposes a customized topology optimization method for generating tensegrity modules tailored to modular assembly applications. The design domain of the target structure is first partitioned into several subregions, within which customized topology optimization of tensegrity modules is conducted using a mixed integer linear programming formulation. The proposed optimization model aims to minimize a combined objective function comprising the number of members and the total strut length, while explicitly incorporating fundamental tensegrity design attributes, including self-equilibrium conditions, unilateral force constraints, Class -k constraints, and so on. Meanwhile, assembly interface constraints are introduced to meet specific modular assembly requirements, and structural integrity constraints based on a single-commodity flow model are imposed to ensure module feasibility. Additional customized design constraints can also be readily integrated into the framework, thereby enabling the generation of novel tensegrity module topologies that precisely satisfy expected development objectives. Several representative numerical examples are presented to demonstrate the effectiveness and versatility of the proposed method. This study opens a new avenue that integrates topology optimization with modular assembly for the design of large-scale tensegrity structures, and it is expected to serve as a methodological reference for advancing the engineering application of complex tensegrity systems.