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On the singularities of constrained tensegrity systems – application to a modified T3 model
Author(s) -
Pirentis A.P.,
Markatis S.,
Lazopoulos K.A.,
Lazopoulos A.K.
Publication year - 2009
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200700152
Subject(s) - tensegrity , singularity , singularity theory , quasistatic process , gravitational singularity , mathematics , simple (philosophy) , branching (polymer chemistry) , mathematical analysis , geometry , physics , materials science , philosophy , epistemology , quantum mechanics , composite material
Singularity theory is applied for the study of constrained tensegrity systems. Previous studies have already been performed on non‐constrained systems; however, the present one allows for general non‐symmetric equilibrium configurations. A modified 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 quasistatic loading. 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 is implemented into the fold catastrophe of the asymmetric configuration of the modified T3 tensegrity model and an elliptic umbilic singularity for the case of compound branching. It is pointed out that singularity studies with constraints demand a quite different mathematical approach than those without constraints.