Stiffness contributions of tension structures evaluated from the levels of components and symmetry subspaces

Abstract

Tension structures are kinematically indeterminate and contain flexible cables. Geometric stiffness of each member induced by its internal force and involved symmetry subspace play an important role in maintaining structural stability. In this paper, stiffness contributions of tension structures are systematically evaluated from the levels of both structural components and symmetry subspaces. Starting from the level of components, we transform the modified elastic stiffness matrix, the geometric stiffness matrix and the tangent stiffness matrix of a structure in combinational contributions from all the members. Then, on the basis of symmetry-adapted stiffness blocks obtained by group theory, all the stiffness characters and directions are neatly extracted from different symmetry subspaces. Three types of stiffness contribution indexes are denoted, and a Geiger cable dome is presented as the illustrative example. It shows that the contribution index evaluated from the level of components clarifies the importance of different members. On the other hand, contribution indexes evaluated from different symmetry subspaces can predict symmetry of lower-order stiffness, and reveal the importance of prestresses in different symmetry spaces.