A marching procedure for form-finding for tensegrity structures

被引:45
作者
Micheletti, Andrea [1 ]
Williams, William O. [2 ]
机构
[1] Univ Roma Tor Vergata, Dipartimento Ingn Civile, I-00133 Rome, Italy
[2] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
关键词
tensegrity structures; stability analysis; rank-deficiency manifold; marching processes; limit placements;
D O I
10.2140/jomms.2007.2.857
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We give an algorithm for solving the form-finding problem, that is, for finding stable placements of a given tensegrity structure. The method starts with a known stable placement and alters edge lengths in a way that preserves the equilibrium equations. We then characterize the manifold to which classical tensegrity systems belong, which gives insight into the form-finding process. After describing several special cases, we show the results of a successful test of our algorithm on a large system.
引用
收藏
页码:857 / 882
页数:26
相关论文
共 55 条
[1]  
Aldrich JB, 2003, P AMER CONTR CONF, P5245
[2]   Implicit function theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworks [J].
Alexandrov, V .
MONATSHEFTE FUR MATHEMATIK, 2001, 132 (04) :269-288
[3]  
[Anonymous], ADAPT STRUCT MAT SYS
[4]   RIGIDITY OF GRAPHS .2. [J].
ASIMOW, L ;
ROTH, B .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1979, 68 (01) :171-190
[5]  
Barnes M. R., 1999, International Journal of Space Structures, V14, P89, DOI [https://doi.org/10.1260/02663519914947, DOI 10.1260/02663519914947, 10.1260/0266351991494722, DOI 10.1260/0266351991494722]
[6]  
BOUDERBALA M, 1998, P IUTAM IASS S DEPL, P5245
[7]  
BURKHARDT RW, 2006, PRACTICAL GUIDE TENS
[8]  
Calladine CR, 1991, INT J SOLIDS STRUCT, V27, P505, DOI 10.1016/0020-7683(91)90137-5
[10]  
Cauchy A L., 1813, Journal de l'Ecole polytechnique, V9, P87