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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >On the singularities of constrained tensegrity systems — application to a modified T3 model
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On the singularities of constrained tensegrity systems — application to a modified T3 model

机译:关于约束张力系统的奇异性—在改进的T3模型中的应用

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摘要

Singularity theory is applied for the study of constrained tensegrity systems. Previous studies have already been performedon non-constrained systems; however, the present one allows for general non-symmetric equilibrium configurations. Amodified T3 tensegrity model comprising seven rigid bars, three elastic cables and one rotational spring is considered.The stability of this model is examined performing singularity theory for deformations under conservative quasistaticloading. Critical conditions for branching of the equilibrium paths are defined and their post-critical behavior is discussed.Classification of the simple and compound singularities of the total potential energy function is effected. The theory isimplemented into the fold catastrophe of the asymmetric configuration of the modified T3 tensegrity model and an ellipticumbilic singularity for the case of compound branching. It is pointed out that singularity studies with constraints demanda quite different mathematical approach than those without constraints.
机译:奇异性理论被用于约束张力系统的研究。先前的研究已经在非约束系统上进行;然而,本发明允许一般的非对称平衡构型。考虑了改进的T3张力模型,该模型包含7条刚性杆,3条弹性电缆和1个旋转弹簧。使用奇异性理论对保守准静态载荷下的变形进行了检验,以验证该模型的稳定性。定义了平衡路径分支的临界条件,并讨论了它们的临界后行为。对总势能函数的简单奇点和复合奇点进行了分类。该理论在改进的T3张力模型的不对称构型的折叠灾难和复合支化情况下的椭圆脐带奇异性方面得到了实现。需要指出的是,具有约束的奇异性研究与没有约束的奇异性研究需要完全不同的数学方法。

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