For an inflatable structure having a flexible outer shell or wall structure having a flexible restraint layer comprising interwoven, load-bearing straps, apparatus for integrating one or more substantially rigid members into the flexible shell. For each rigid member, a corresponding opening is formed through the flexible shell for receiving the rigid member. A plurality of connection devices are mounted on the rigid member for receiving respective ones of the load-bearing straps. In one embodiment, the connection devices comprise inner connecting mechanisms and outer connecting mechanisms, the inner and outer connecting mechanisms being mounted on the substantially rigid structure and spaced along a peripheral edge portion of the structure in an interleafed array in which respective outer connecting mechanisms are interposed between adjacent pairs of inner connecting mechanisms, the outer connecting mechanisms projecting outwardly from the peripheral edge portion of the substantially rigid structure beyond the adjacent inner connecting mechanisms to form a staggered array of connecting mechanisms extending along the panel structure edge portion. In one embodiment, the inner and outer connecting mechanisms form part of an integrated, structure rotatably mounted on the rigid member peripheral edge portion.