Abstract The structural stiffness of a tensegrity is dominated not only by the material stiffness, but also by its internal forces. The deployment of tensegrities with member length actuation is investigated with an emphasis on the variation in the structural load-carrying stiffness. The relationship between the driving elongation of members and the structural displacement is established. The analytical incremental expressions for the elastic stiffness matrix and the geometrical stiffness matrix with respect to the driving elongation of members are given. The variation in the load-induced elastic deformation can thus be evaluated for a tensegrity being deployed. A basic equation that satisfies both the equilibrium condition and the load-carrying stiffness constraints is established and used to trace the equilibrium configurations on the deployment path step by step. The solutions for the driving elongation of members are discussed for the objectives of producing the shortest actuation distance and reducing the driving energy, respectively. A numerical strategy is suggested to correct the errors caused by the linear assumptions that are introduced in the derivation of the basic equation. The proposed method is employed to analyse the deployment of an illustrative cantilever tensegrity subjected to load-carrying stiffness constraint, and the results verify its validity. When the objective of reducing the driving energy is adopted, the cantilever tensegrity exhibits an adaptive deformation capability to maintain the constant load-induced deflection at its end joint throughout the deployment process.

中文翻译：

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受承载刚度约束的张拉整体的部署

摘要 张拉整体的结构刚度不仅受材料刚度的支配，还受其内力的支配。研究了具有构件长度驱动的张拉整体的部署，重点是结构承载刚度的变化。建立了构件的驱动伸长与结构位移之间的关系。给出了弹性刚度矩阵和几何刚度矩阵关于构件驱动伸长的解析增量表达式。因此，可以针对正在展开的张拉整体评估负载引起的弹性变形的变化。建立了满足平衡条件和承载刚度约束的基本方程，并用于逐步跟踪部署路径上的平衡配置。分别针对产生最短驱动距离和降低驱动能量的目标，讨论了构件驱动伸长的解决方案。提出了一种数值策略来纠正由基本方程推导中引入的线性假设引起的误差。所提出的方法用于分析受承载刚度约束的说明性悬臂张拉整体的部署，结果验证了其有效性。当采用降低驱动能量的目标时，