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Abstract This paper presents conditions for self-equilibrium as well as super-stability of the truncated regular hexahedral and octahedral tensegrity structures. Their symmetry can be described by octahedral group in group representation theory, and furthermore, their force density matrix is analytically rewritten in the symmetry-adapted form. The condition for self-equilibrium, in terms of force densities, is found by satisfying the non-degeneracy condition for a tensegrity structure. The condition for super-stability, also in terms of force densities, is further presented by guaranteeing positive semi-definiteness of the force density matrix. [ABSTRACT FROM AUTHOR]

An optimization approach is presented for force design of tensegrity structures by enumeration of the vertices of the feasible region of the prestresses, which is defined as the linear combinations of the coefficients of the self-equilibrium force vectors. The unilateral properties of the stresses in cables and struts are taken into consideration. In order to design the stiffest structure against uncertain external loads as well as specific external loads, a multiobjective optimization problem is formulated for simultaneous maximization of the lowest eigenvalue of the tangent stiffness matrix and minimization of the compliance against a specified set of external loads. In the numerical example, Pareto optimal solutions are found by enumerating the vertices of the feasible region of prestresses of a tensegrity grid, and the monotonicity properties of the objective functions are investigated. [ABSTRACT FROM AUTHOR]

Abstract: Stability conditions for tensegrity structures are derived based on positive definiteness of the tangent stiffness matrix, which is the sum of the linear and geometrical stiffness matrices. A necessary stability condition is presented by considering the affine motions that lie in the null-space of the geometrical stiffness matrix. The condition is demonstrated to be equivalent to that derived from the mathematical rigidity theory so as to resolve the discrepancy between the stability theories in the fields of engineering and mathematics. Furthermore, it is shown that the structure is guaranteed to be stable, if the structure satisfies the necessary stability condition and the geometrical stiffness matrix is positive semidefinite with the minimum rank deficiency for non-degeneracy. [Copyright &y& Elsevier]

Abstract: In the process of designing a tensegrity system, some constraints are usually introduced for geometry and/or forces to ensure uniqueness of the solution, because the tensegrity systems are underdetermined in most cases. In this paper, a new approach is presented to enable designers to specify independent sets of axial forces and nodal coordinates consecutively, under the equilibrium conditions and the given constraints, to satisfy the distinctly different requirements of architects and structural engineers. The proposed method can be used very efficiently for practical applications because only linear algebraic equations are to be solved, and no equation of kinematics or material property is needed. Some numerical examples are given to show not only efficiency of the proposed method but also its ability of searching new configurations. [Copyright &y& Elsevier]

Abstract: This paper presents analytical formulations for the symmetry-adapted equilibrium, force density and geometrical stiffness matrices for prismatic tensegrity structures with dihedral symmetries. An analytical expression for the infinitesimal mechanisms is also derived. [Copyright &y& Elsevier]