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This study formulates numerical and analytical approaches to the self-equilibrium problem of novel units of tensegrity metamaterials composed of class θ = 1 tensegrity prisms. The freestanding configurations of the examined structures are determined for varying geometries, and it is shown that such configurations exhibit a large number of infinitesimal mechanisms. The latter can be effectively stabilized by applying self-equilibrated systems of internal forces induced by cable prestretching. The equilibrium equations of class θ = 1 tensegrity prisms are studied for varying values of two aspect parameters, and local solutions to the self-equilibrium problem are determined by recourse to Newton–Raphson iterations. Such a numerical approach to the form-finding problem can be easily generalized to arbitrary tensegrity systems. An analytical approach is also proposed for the class θ = 1 units analyzed in the present work. The potential of such structures for development of novel mechanical metamaterials is discussed, in the light of recent findings concerned with structural lattices alternating lumped masses and tensegrity units.

本研究针对由θ=1类张拉整体棱柱（class θ = 1 tensegrity prisms）构成的新型张拉整体超材料（tensegrity metamaterials）单元的自平衡问题，构建了数值与解析求解方法。针对不同几何参数下的目标结构，确定了其独立构型，并证明此类构型存在大量无穷小机构（infinitesimal mechanisms）。通过施加由索预应力（cable prestretching）诱导的自平衡内力系统，可有效稳定这类无穷小机构。针对θ=1类张拉整体棱柱的平衡方程，结合两类形状参数的不同取值开展研究，并借助牛顿-拉夫逊迭代法（Newton–Raphson iterations）求解自平衡问题的局部解。这类用于找形问题（form-finding problem）的数值求解方法可轻松推广至任意张拉整体系统。本研究同时针对所分析的θ=1类单元提出了解析求解路径。结合近期关于交替布置集中质量块（lumped masses）与张拉整体单元的结构晶格的相关研究进展，讨论了此类结构在开发新型力学超材料（mechanical metamaterials）领域的应用潜力。