In this study, through a scheme combining theoretical analysis, numerical simulation and optimization algorithm, the influence law of different load acting positions on the structural stiffness matrix is investigated, and a multi-objective topology optimization design framework based on the genetic algorithm of small habitats is proposed. Firstly, the tensioned overall structural stiffness matrix is derived, which leads to the judgment conditions of the tensioned overall structural stability and zero-stiffness displacement mode. The optimization objective is set to minimize the total mass of the structure, and the topology optimization of the tensioned overall structure is carried out. The shared function small habitat technique and pre-selection mechanism are adopted to solve the stable modes of the tensioned monolithic structure under different conditions. Then the nonlinear evolution characteristics of nodal displacement and stiffness under various typical loads are analyzed using a quadrangular tensile monolithic structure as the research object. The evaluation results revealed that the structure with a grouping number of 12 has an optimal overall performance with a percentage area of 59.25%. At the same time, the structure with this grouping is also the structure with the lowest sensitivity and the strongest robustness, which indicates that the optimization strategy in this paper effectively designs the tensioned monolithic structure with high structural adaptability. This study provides theoretical basis and methodological support for the design and optimization of the performance of tensioned monolithic structures under different loading environments.
