Reserve of analytical surfaces for architecture and construction

After a period of relative calm in the construction and design of thin-walled largespan shells and network multilayer shell structures, which, according to the world's leading architects, began in the 1980 s, the time has come for the expanded use of spatial structures in the architecture of public and industrial buildings. Less commonly, shells are used in small-sized housing construction: ecological villages, noospheric and bionic architecture. The entire 20th century did not stop research on the development of analytical and numerical methods for analyzing shells for strength and stability, for the creation of new building materials. Geometers have created and studied more than 600 analytical surfaces that can be mistaken for the mid-surfaces of civil and mechanical engineering shells. As a result, by the beginning of the 21st century, architects and engineers had all the necessary tools to continue the traditions of the "golden age of shells". The analysis of problems with the use of new forms in parametric architecture, carried out in the article, showed that more than ten classes of surfaces from their classification have not yet found application in architecture and mechanical engineering. It is assumed that the number of applied classes of surfaces will not expand, and new ideas for the shaping of shells will be based on the use of already well-known surfaces, namely, surfaces of revolution, transfer, umbrella, minimal, ruled and wavy surfaces. Mainly, shell structures will be designed taking into account environmental, energy-saving requirements and transforming structures.

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