Let’s think of a paper sheet. If we tried to stiffen it from its primary state, it couldn’t support its own weight. However, if we bend it, the sheet achieves a new structural quality. The shells act in the same way. “You can’t imagine a form that doesn’t need a structure or a structure that doesn’t have a form. Every form has a structure, and every structure has a form. Thus, you can’t conceive a form without automatically conceiving a structure and vice versa”.  The importance of the structural thought that culminates in the constructed object is then, taken by the relationship between form and structure. The shells arise from the association between concrete and steel and are structures whose continuous curved surfaces have a minimal thickness; thus they are widely used in roofs of large spans without intermediate supports.
In structural terms, they are efficient because they resist compression efforts and absorb at specific points on their surface, especially near the supports — small moments of flexion.
Present-day shells originate from Egyptian, Assyrian, and Roman civilizations, in which arched and vaulted structures were erected, using stone masonry and rudimentary types of concrete as the building material. The Pantheon in Rome and the Basilica of Hagia Sophia in Istanbul are spectacular examples that remain to this day. In those times, there was no structural calculation as we know it today; the buildings were erected using practical and empirical knowledge acquired by professionals through observation and repetition of procedures. Currently, modern computational models are used, such as the finite element method (FEM), which greatly assists in the design of these structures. After some time without significant advances in construction methods, shells evolved enormously from the beginning of the XX century, with the improvement of the reinforced concrete: a moldable material, very resistant to compression, bending, and in a certain way, traction.
Modern shells were first introduced by architects and engineers such as Eugène Freyssinet (1879-1962), Bernardo Laffaielle (1900-1955), Pier Luigi Nervi (1891-1979), Eduardo Tarroja (1899-1961), Félix Candela (1910-1997), among others. They introduced innovative theories of design and execution of works, allowing the construction of remarkable structures of double curvature, such as the hyperbolic paraboloid that covers the restaurant of the City of Arts and Sciences in Valencia, Spain, designed by Candela.
Oscar Niemeyer‘s (1907-2012) Pampulha Modern Ensemble is considered the precursor of concrete shells in Brazil, an influence for many other projects that use the same constructive process in the country and around the world.
It is interesting how modern shells have a structural display similar to membranes, but just in an inverted way. That is to say, whereas in membranes the efforts are almost exclusively of traction, when being inverted, or “turned upside down,” these efforts become compression. From then on, concrete is the ideal material to resist them. Antoni Gaudi (1852-1926) used this process to carry out his projects.
Shells manage to resist large compression loads evenly distributed over their surface, however, due to their minimum thickness, they have little tensile strength and shouldn’t receive concentrated loads. The load distribution on the surface is represented by the weight of the structure, the coating materials, and the wind pressure.
In summary, we can say that a shell structure is a continuous curved surface where the thickness is much smaller than the other dimensions. The structural behavior is divided into two: the theory of the membrane and the theory of flexion. In the first, the resistance of the membrane is considered, which results in requests for normal forces and shear stress. In the second, the flexures that result from the curved shell are considered: requests for moments, normal stresses, shear and longitudinal shear. In shell projects, special attention must be paid to supports, since significant flexion requests may occur in these areas. 
In the 1960s there was an apogee of the construction of large shells. Its use went into decline due to the high costs of labor, concrete, and methods of formwork that could hardly be reused in another similar work. The shells, being of little thickness, require constant maintenance to prevent leaks and other construction pathologies. Since the 1980s, the preference for polygonal shapes and stretched structures occurred.
Next, selected iconic projects with concrete shells:
 (REBELLO, 2000, p. 26).
 (MEDRANO; MEIRELLES, 2005)
REBELLO, Y. A Concepção Estrutural e a Arquitetura. 9. ed. São Paulo: Zigurate, 2000.
REBELLO, Y. Bases para Projeto Estrutural na Arquitetura. 4.ed. São Paulo: Zigurate, 2007.
MEDRANO, R. H.; MEIRELLES, C. R. M.: 2005, Estruturas Espaciais em Cascas: Estudo de Casos Latino-Americano, In: XXI Conferência Latinoamericana de Escuelas y Facultades de Arquitectura – CLEFA, Loja.
TEIXEIRA, Pedro Wellington G. N.; DE HANAI, João Bento. Projeto e execução de coberturas em casca de concreto com forma de membrana pênsil invertida e seção tipo sanduíche. Cadernos de Engenharia de Estruturas, São Carlos, n. 19, p.101-131, 2002.