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A `!shell`! is a three-dimensional solid `F33f`_`[structural element`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Structural_element]`_`f whose thickness is very small compared to its other dimensions. It is characterized in structural terms by mid-plane stress which is both coplanar and normal to the surface. A shell can be derived from a `F33f`_`[plate`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Plate_(structure)]`_`f in two steps: by initially forming the middle surface as a singly or doubly curved surface,`:cite-ref-z05-1-0[`F5bf`_`[1`#cite-note-z05-1]`_`f] then by applying loads which are coplanar to the plate's `F33f`_`[plane`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Plane_(geometry)]`_`f thus generating significant stresses. Materials range from concrete (a `*`F33f`_`[concrete shell`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Concrete_shell]`_`f`*) to fabric (as in `*`F33f`_`[fabric structures`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Fabric_structure]`_`f`*).

`!Thin-shell structures`! (also called `!plate and shell structures`!) are lightweight constructions using `F33f`_`[shell elements`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=List_of_structural_elements]`_`f. These elements, typically curved, are assembled to make large structures. Typical applications include aircraft `F33f`_`[fuselages`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Fuselage]`_`f, boat hulls, and the `F33f`_`[roofs`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Roof]`_`f of large buildings.

>>Contents

• `F0af`_`[Definition`#definition]`_`f
• `F0af`_`[Types`#types]`_`f
• `F0af`_`[See also`#see-also]`_`f
• `F0af`_`[References`#references]`_`f
• `F0af`_`[Further reading`#further-reading]`_`f
• `F0af`_`[External links`#external-links]`_`f

-─

>>Definition

A thin shell is defined as a shell with a thickness which is small compared to its other dimensions and in which deformations are not large compared to thickness. A primary difference between a shell structure and a plate structure is that, in the unstressed state, the shell structure has curvature as opposed to the plates structure which is flat. `F33f`_`[Membrane`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Tensile_structure]`_`f action in a shell is primarily caused by in-plane forces (`F33f`_`[plane stress`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Plane_stress]`_`f), but there may be secondary forces resulting from flexural deformations. Where a flat plate acts similar to a beam with bending and `F33f`_`[shear stresses`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Shear_stress]`_`f, shells are analogous to a cable which resists loads through tensile stresses. The ideal thin shell must be capable of developing both tension and compression.`:cite-ref-2[`F5bf`_`[2`#cite-note-2]`_`f]

>>Types

The most popular types of thin-shell structures are:

• `F33f`_`[Concrete shell`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Concrete_shell]`_`f structures, often cast as a `F33f`_`[monolithic dome`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Monolithic_dome]`_`f or `F33f`_`[stressed ribbon bridge`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Stressed_ribbon_bridge]`_`f or `F33f`_`[saddle roof`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Saddle_roof]`_`f
• Lattice shell structures, also called `F33f`_`[gridshell`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Gridshell]`_`f structures, often in the form of a `F33f`_`[geodesic dome`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Geodesic_dome]`_`f or a `F33f`_`[hyperboloid structure`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Hyperboloid_structure]`_`f
• `F33f`_`[Membrane structures`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Membrane_structure]`_`f, which include `F33f`_`[fabric structures`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Fabric_structure]`_`f and other `F33f`_`[tensile structures`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Tensile_structure]`_`f, cable domes, and `F33f`_`[pneumatic structures`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Pneumatic_structure]`_`f.

>>See also

• `F33f`_`[Monocoque`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Monocoque]`_`f
• `F33f`_`[Diagrid`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Diagrid]`_`f
• `F33f`_`[Stretched grid method`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Stretched_grid_method]`_`f
• `F33f`_`[List of thin-shell structures`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=List_of_thin-shell_structures]`_`f

`!Persons related:`!

• `F33f`_`[Félix Candela`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Félix_Candela]`_`f
• `F33f`_`[Dyckerhoff & Widmann`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Dyckerhoff_&_Widmann]`_`f
• `F33f`_`[Wilhelm Flügge`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Wilhelm_Flügge]`_`f
• `F33f`_`[Eugène Freyssinet`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Eugène_Freyssinet]`_`f
• `F33f`_`[Heinz Isler`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Heinz_Isler]`_`f
• `F33f`_`[Pier Luigi Nervi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Pier_Luigi_Nervi]`_`f
• `F33f`_`[Plate`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Plate_(structure)]`_`f
• `F33f`_`[Frei Otto`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Frei_Otto]`_`f
• `F33f`_`[Ernest Edwin Sechler`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Ernest_Edwin_Sechler]`_`f
• `F33f`_`[Vladimir Shukhov`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Vladimir_Shukhov]`_`f

• `F33f`_`[All-Russia Exhibition 1896`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=All-Russia_Exhibition_1896]`_`f

• `F33f`_`[Eduardo Torroja`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Eduardo_Torroja]`_`f
• `F33f`_`[Membrane theory of shells`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Membrane_theory_of_shells]`_`f

>>References

`:cite-note-z05-1`!1.`! `F0af`_`[↑`#cite-ref-z05-1-0]`_`f `:citerefo-c-zienkiewicz-and-r-l-taylor`aO.C. Zienkiewicz and R.L. Taylor. `*The finite element method for solid and structural mechanics`*.
`:cite-note-2`!2.`! `F0af`_`[↑`#cite-ref-2]`_`f `:citerefchenlui2005`aChen, Wai-Fah; Lui, E. M., eds. (2005-02-28). `*Handbook of Structural Engineering, Second Edition`* (2 ed.). Boca Raton: CRC Press. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 9780849315695.

>>Further reading

• `:citerefbechthold2008`aBechthold, Martin (2008-03-20). `*Innovative Surface Structures: Technologies and Applications`* (1 ed.). Abingdon: Taylor & Francis. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 9780415419673.
• `:citerefsuchov1990`aSuchov, Vladimir G. (1990). Rainer Gaefe (ed.). `*VLADIMIR G. SUCHOV 1853-1939; Die Kunst Der Sparsamen Konstruktion`* (1st ed.). Stuttgart: Deutsche Verlags-Anstalt. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 9783421029843.

>>External links

Wikiquote has quotations related to

Thin-shell structure

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Wikimedia Commons has media related to

Thin-shell structures

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• Thin-shell structures
• Double thin-shells structures
• Hypar & Concrete Shells
• Past and Future of Grid Shell Structures
• Shape optimization of Shell and Spatial structure (PDF)
• Lattice Shell for Space Vehicles (PDF)
• International Association for Shell and Spatial Structures

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