Mathematical Chemistry Approaches for Computer-Aid Design of Free-Shaped Structures in Architecture and Construction Engineering

The use of computers in architecture and construction engineering simplifies and automatize many manual operations, especially in the case of curved surfaces such as shell structures. Moreover, it allows fast screening and characterization of many technical solutions through computer-solving equations and the verification of buildings and metallic structures stabilities in different weather and seismic conditions. In parallel, significant efforts have been made to characterize and explore carbon-based nanosystems. Important mathematical concepts and methods were developed for the description of such structures in the frame of mathematical chemistry. Because the lattice topology of shell structures in architecture and nanosystems in chemistry are similar, it is possible to transfer well-established theoretical concepts and knowledge of using nanosystems to the design of shell structures. The topologies of the nanosystems are characterized by lower densities of edges per node offering better solutions for curved surfaces than the typical grids used in architecture. As far as we know, no such connections between the topologies of nanosystems and shell structures have been established before. This transfer would be helpful for increased accuracy and speed in finding the best technical solutions for the building’s design. In this paper, we identify and propose for the design of the shell structures several mathematical approaches developed for atomistic systems.