Analytical form-finding of tensegrities using determinant of force-density matrix. (1st April 2018)

• Record Type: Journal Article
• Authors: Zhang, Li-Yuan; Zhu, Shi-Xin; Li, Song-Xue; Xu, Guang-Kui
• Is Part Of: Composite structures. Volume 189(2018)
• Page Start: 87
• Page End: 98
• Publication Date: 2018-04-01
• Subjects: Tensegrity -- Analytical form-finding -- Force-density -- Matrix determinant; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2018.01.054
• Languages: English
• ISSNs: 0263-8223

Abstract

Abstract: Tensegrities have found great importance and numerous applications in many civil, aerospace and biological systems, and form-finding analysis is a vital step to obtain their self-equilibrated configurations before applying external loads. In this paper, we present a concise and general analytical scheme for tensegrity form-finding analysis. Additions and multiplications are employed as major computational operations, that can guarantee the solving process computationally efficient. Based on the characteristic polynomial of the symbolic force-density matrix, the two (three) lower-order coefficients that are necessary for the form-finding of planar (three-dimensional) tensegrities are expressed by a unified compact equation using the matrix determinants. The force-densities of tensegrity elements satisfying the established equation can determine the self-equilibrated state of tensegrity. A large number of representative planar and three-dimensional examples are analyzed to verify the validity and efficiency of our analytical form-finding method. The predictions of our scheme are in broad agreement with the results obtained by many other methods. This study produces continuously variable force-densities of self-equilibrated tensegrities, and helps to design their unusual mechanical properties for scientific and engineering applications.