Flexural tensegrity

Abstract

The expression "flexural tensegrity" indicates an assembly of stiff segments held together by the tying action of prestressed tendons passing through them, in such a way that the integrity under flexure is provided by the tensile members (tendons). The key point is that the contact surfaces of any pair of consecutive segments are shaped according to properly-designed pitch profiles, such that a large relative rotation of the segments is allowed. As a result, the joints open up under bending, and this produces the straining of the tendons, which are free to move in properly-shaped cavities inside the segments and are anchored only to the ends of the beam (unbonded cables). The elongation of each cable, to an amount dictated by the shape of the contact surfaces, thus affects the elastic energy of the system and, hence, characterizes the constitutive bending properties of the segmental assembly, as a function of the design shape of contact profiles, as well as of the prestress and axial stiffness of the cable. A variational approach can be used to find the set of nonlinear equations that govern the response of the structural system, both in the static and dynamic equilibrium states.

The flexural-tensegrity concept can be explored in many forms. By changing the shape of the contact profiles, linear, sub-linear or super-linear constitutive responses can be obtained. As a function of the tendon stiffness, nonlinear Duffing-like vibrations are attained and can be controlled by varying the axial force in the tendon. Enhancing the mobility of the tendon in large cavities, the bending energy can be made non-convex in type, possibly achieving complex snap-through sequential motions. The limit, when the number of segments goes to infinity and their length to zero, corresponds to a particular type of Euler's elastica with nonlocal response, whose bent shape can be computed analytically (with elliptic integrals), or numerically. Field applications, yet to be fully explored, have been found in archery (a new type of deployable segmental bow) and soft robotics (limbs controlled by internal/external cables). Multi-stable flexural tensegrities can be used as basic constituents for metamaterials with tailored 3D mechanisms, in the form of plates and cubes, and for propulsion in fluids as flagellating tails. Larger scale applications in kinetic architecture, yet to be fully appreciated, can be found in the manufacturing of movable skeletons and envelopes. In the field of industrial design, the concept has been used in the manufacturing of a desk lamp, where the bent shape of the arm can be tuned by varying the tension force in the pair of prestressing cables, which also convoy electricity.

As a hint for future research, a different kinematics is finally introduced and preliminary investigated. This corresponds to the sliding of plates on initially-matching wavy contact surfaces (rather than rolling along pitch profiles), thus constituting the basis for the new concept of "shear tensegrity". The model can specifically find application in the interpretation of the mechanical behavior of nacre-like laminates.