Free-Form, Doubly Curved, and Special-Shaped Building Structures: An Evidence Map for Integrated Design, Structural Performance, and Fabrication

Designing free-form, doubly curved, and special-shaped building structures requires geometry, structural verification, and fabrication to be reconciled, but evidence for these linked decisions is dispersed across disciplines. This review develops a documented evidence map and focused critical synthesis of method–typology links for integrated building design. A Scopus search on 25 July 2026 returned 3489 records; deduplication left 3413, title screening retained 3058; and rule-based title, abstract, and metadata classification produced a 1493-record mapping pool. A purposive 89-study synthesis corpus combined 40 query-traceable and 49 curated records across six engineering axes. Force density, surface stress density, and dynamic relaxation methods remain the main form-finding families, with their suitability dependent on structural typology and construction route. Isogeometric and semi-analytical formulations can reduce geometry-transfer approximation, whereas conventional finite-element workflows predominate in practice. Evidence is strongest for the stability of canonical and single-layer reticulated shells; dynamic studies remain concentrated on spherical domes. Fabrication research addresses knitted formwork, robotic spraying, additive manufacturing, cold-bent glass, and component rationalisation, but few studies close the design–analysis–fabrication loop. By linking methods to structural typologies and distinguishing the mapping pool from the selected full-text corpus, this review offers an auditable basis for qualified method selection and identifies priorities for transferable verification without claiming exhaustive coverage.