Equivalent Continuum Model for Deployable Flat Lattice Structures

Deployable structures can be stored in a compact, folded configuration and are easily deployed into load-bearing, open forms. Hence, they are suitable for applications where speed and ease of erection and reusability are desired. The structures investigated here are prefabricated space frames made of so called scissor-like elements, sets of two straight bars connected to each other by a pivot. These structures are stress-free and self-standing in both their folded and deployed configurations, thus overcoming major disadvantages of previous designs. This study deals with deployable structures that are flat and subjected to normal loads in their deployed configuration. Although the behavior for that loading case is linear, the availability of an equivalent continuum model for stiffness prediction is desirable because it can significantly reduce the computational effort during preliminary design. The derivation of such a model is not straightforward because of the unorthodox geometry and the rotations allowed by the hinged and pivotal connections. This problem is addressed by first applying the direct stiffness method within a symbolic manipulation framework to transform the lattice structure to an equivalent single-layer grid, and then using existing expressions to obtain the desired equivalent plate. The model exhibits good accuracy and convergence characteristics for uniform loads.