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This paper investigates the architectural and structural potential of folded-smooth (F-S) hybrid shell structures, modeled using the Takagi-Landsberg (TL) function and Iterated Function Systems (IFS) to achieve smooth transitions between folded and smooth surfaces. Using a hyperbolic paraboloid (hypar) profile, the study evaluates the distinct structural behaviors of F-S configurations. Finite element analysis shows that lateral F-S shells with folded ends at the ground achieve comparable stability to smooth hypars, while longitudinal F-S shells with unsupported ends show structural weaknesses, particularly at flying edges. Despite construction challenges, the study demonstrates that F-S shells combine structural robustness and aesthetic flexibility, advancing design possibilities in hybrid architectural forms. [ABSTRACT FROM AUTHOR]