While trying to think of how the structure must be, several examples of deployable structures passed infront of my eyes. From simple deployments to snap-through structures, which use buckling as mechanical factor for configuration.
First of all, the structure should have such a geometry that, at the same time it enables the contraction and deployment, is compatible with the environmental control elements (cladding or any other element that will serve for sunlight and rain control).
As a fisrt approach, a geometry was chosen that can, at first sight, achieve the configurations. This image shows a series of deployable arches that, when placed together, form a roof. A similar geometry can be taken into considereation for reproducing the desired configurations.
Another aspect of the structure should be the tesselation that would be chosen in order to cover the space. There are some kinds of tesselations that are more appropiate to use for planar, or at least, single curved structures. If the structure is double curved or has a free form, some other tesselations, or even diferent shape modules, should be necessary to achieve the final form.
In terms of ease for study the behavior of such a desired structure, first I will work with regular modular shapes. Therefore I am currently searching the posibilities of an hexagonal module and the way it fills a curved shape. Maybe after some geometric analysis, I find more appropiate to slightly change the module of completely replace it with other geometrical shape.
The main concerns at this point are two: 1. how to create a structure taht can also be compatible with the cladding: and 2. How would the two wings of the structure adapt to each other in order to work as one structural entity.