Geometric effects in an elastic tensegrity structure

Tensegrity structures are under-constrained, 3-dimensional, self-stressing structural systems. They demonstrate an infinitesimal flex and when loaded they display a nonlinear geometric stiffening. In earlier work many examples of the resulting force-displacement relationship have been demonstrated numerically, and some aspects of the force-displacement relationship have been derived analytically. In this article an energy formulation is presented for the case of a simple but representative tensegrity structure, yielding an exact solution for the force-displacement relationship. The solution makes understandable the different appearance of the force-displacement relationship when comparing a system at zero prestress to one at high prestress, or when comparing a system with almost-inextensible members to one with highly extensible members. The exact solution also is offered as a benchmark against which numerical solutions should be tested. Furthermore, the formulation and the solution reveal conditions of asymmetry of response that have not been noted previously.