Abstract
An analytical form-finding method for regular tensegrity structures based on the concept of force density is presented. The self-equilibrated state can be deduced linearly in terms of force densities, and then we apply eigenvalue decomposition to the force density matrix to calculate its eigenvalues. The eigenvalues are enforced to satisfy the non-degeneracy condition to fulfill the self-equilibrium condition. So the relationship between force densities can also be obtained, which is followed by the super-stability examination. The method has been developed to deal with planar tensegrity structure, prismatic tensegrity structure (triangular prism, quadrangular prism, and pentagonal prism) and star-shaped tensegrity structure by group elements to get closed-form solutions in terms of force densities, which satisfies the super stable conditions.
Highlights
Tensegrity structures refer to the stable structures that are based on the balance between their members in compressive or tensile states
The paper is organized as follows: Section 2 illuminates the basic concept of force density method and its usage in the process of form-finding, which is followed by the non-degeneracy condition
The process of the analytical form-finding method can be divided into assumptions (Section 4.1), equilibrium analysis (Section 4.2) and super-stability examination (Section 4.3) in terms of force densities
Summary
Tensegrity structures refer to the stable structures that are based on the balance between their members in compressive or tensile states. Shape design is usually based on force density method, dynamic relaxation method, or nonlinear structural analysis. Numerical methods with force density concepts have been developed [41,42] It may turn into a nonlinear problem that intends to minimize the total length of cables or maximize that of struts [43]. Though numerical methods can deal with more irregular and complicated structures, analytical methods appear to be the most effective way without iteration or the introduction of concepts from other disciplines It provides an opportunity of looking inside the relation between different force densities. The paper is organized as follows: Section 2 illuminates the basic concept of force density method and its usage in the process of form-finding, which is followed by the non-degeneracy condition. Examples of a planar tensegrity structure, three kinds of prismatic tensegrity structure (triangular prism, quadrangular prism, and pentagonal prism) and a star-shaped tensegrity structure are given in Section 5 to verify its efficiency and versatility
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