Bionics in architecture and geometric modelling of thin shell surfaces

Abstract

In the scientific problem of design and calculation of thin elastic shells in the modern world, certain advances have already been made in mathematical and technical theory, based on hypotheses, experimental data, calculation equations and engineering calculations. Only such shells, which are designed based on calculation and used in building and technical constructions, can be referred to a small number of geometric surfaces. When designing thin shells, surfaces of rotation (sphere, torus, paraboloid, ellipsoid of rotation) and transfer surfaces (hyperbolic and elliptic paraboloid, circular transfer surface) are used. Trends in construction and engineering seek to apply complex mathematical models in harmony with environmental policy and the environment. This leads to the necessity of studying the influence of parameters when modeling an object on the parameters and properties of the created construction. Possessing a more complex shape the shells are realized as a result of experiment. As a result of active introduction of information technologies it became possible to introduce cardinally new methods in the application of geometric thin-walled spatial structures for the design of building and technical constructions, a number of machine-building parts. Modern analytical calculation programs and computer-aided design systems (Compass, Autocad, Archicad, etc.) make it possible to create a geometric projection model of a structure on the basis of primitives, to perform structural and static calculations of a project in an elementary manner. The solution of such layout problems is made possible with the support of computer geometry based on descriptive and analytical geometry, linear and vector algebra, mathematical analysis, and differential geometry. Modern bionics and environmental policy relies on the latest methods of mathematical modeling of architectural projects with a wide choice of computational and graphical software for calculation and 3d visualization.