In an inflatable structure, a plurality of fibers is formed in a cavity of a flexible shell. When structure is inflated, the shell expands and the fibers are tensioned to constrain the flexible shell to have a fiber-constrained shape. When the structure is uninflated, the flexible shell is configured to collapse. The structure is formed by additive manufacturing. The fibers are fused to the shell and can run in various directions in relation to each other and the flexible shell. Fibers can extend obliquely to the shell when tensioned and at crosswise directions in relation to each other to form a nonwoven mesh.