Shell structures have been constructed since ancient times. The Panthe — Thin-shell structure

"While size and support conditions have an important bearing on the degree of accuracy needed in the analysis, the distribution of load has a less important effect on stresses. This is due to the fact that s in the shell are more closely related to the boundary conditions than to the load. Hence, it is usually unnecessary to analyze a thin shell for partial live loads even though the supporting members must be analyzed for such partial loads. For this reason, snow load on thin shells may be assumed either uniformly distributed on the horizontal projection or uniformly distributed over the surface of the shell. On the other hand, local bending moments due to large concentrated loads on the shell must be considered."

"The method of geometric modeling of multi-shell roofs depends mostly on the surfaces properties forming the shell; their curvature, as well as continuity between them. ...s play a specific role, due to their characteristics. Catalan surfaces are s... They are oblique ruled surfaces which can be divided into two groups... second order—hyperbolic paraboloid... [and] of more than second order—s, cylindroids... The difference between hyperbolic paraboloid, conoid, and cylindroid results from different path of movement of a surfaces ruling during formation. In all cases of Catalan surfaces creation... each ruling is parallel to the fixed plane (not containing the surfaces directrices)."

"Thin shells — Three-dimensional spatial structures made up of one or more curved slabs or folded plates whose thicknesses are small compared to their other dimensions. Thin shells are characterized by their three-dimensional load-carrying behavior, which is determined by the geometry of their forms, by the manner in which they are supported, and by the nature of the applied load."

"I have selected the use of hanging models to simulate compressive forces. This is one of the longest-used form finding techniques. It has its roots in physical models, but in recent years it has also given rise to a range of digital tools that are fairly accessible to an uninitiated designer... Hanging models... can be used to simulate... funicular structures. ...derived from the Latin word for “rope”... a structure takes its shape in response to the magnitude and location of forces acting upon it. For example, a rope suspended from two level points will form a “V” when a single point load is added at midpoint, but will form a catenary when under an evenly-distributed load. While a suspended rope is a purely tensile system, if inverted and made rigid that same form converts into a system that is in pure compression. This was first postulated (and wonderfully expressed) by the English scientist Robert Hooke... The value of a structure that is purely in compression is that it experiences no due to structural loads. With no bending present materials can be used very efficiently, allowing for the use of extremely thin elements... materials that are strong in compression... as tiles or masonry, can... be employed."

"The shell designer seeks forms to carry the applied loads in axial compression with minimal bending forces. The earliest example of structural form finding for an arch was published by the English engineer and scientist, Robert Hooke... 1676... As hangs the flexible line, so but inverted will stand the rigid arch. ...Hookes law of inversion, can be extended... and considered for shell structures of various geometries. In the context of shell structures, the term funicular means tension-only or compression-only for a given loading, typically considered... Unlike the case of the hanging cable with a single funicular form... hanging membranes have multiple possible forms. ...[T]he three dimensional shell can carry a wide range of different loadings through membrane behaviour without introducing bending. ...[A] three-dimensional model of intersecting chains could be... used to design a design a discrete shell, in which elements are connected at nodes, or the model could be used to help define a continuous surface. If hanging from a circular support, the model-builder could create a network of meridional chains and hoop chains. By adjusting the length of each chain, various tension-only solutions can be found... Once inverted, this geometry would represent a compression-only form. Such... would quickly illustrate that many different shell geometries can function in compression due to self-weight."

"has designed some of the most striking thin shells in reinforced concrete of the second half of the twentieth century. He creates thin shells by hanging small membranes in tension and creating smooth curving surfaces that are then inverted and scaled up to create large-scale structures in compression. ...Within the constraint of economy, he discovered new forms from purely structural considerations and demonstrated the unlimited possibilities for thin compression shells to be found in hanging models."