Analytical form-finding of tensegrities using determinant of force-density matrix

• DOI: 10.1016/j.compstruct.2018.01.054
• Publication Date: 2018-02-23T15:37:30Z
• Authors: Li-Yuan Zhang; Shi-Xin Zhu; Song-Xue Li; Guang-Kui Xu
• Keywords: Tensegrity; Matrix (chemical analysis); Force density

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.