Theory of architecture
|Babich Vladimir N.|
C.Sc. (Technology), Professor,
GEOMETRIZATION OF FORMS AND STRUCTURES OF CIVIL ENGINEERING OBJECTS AND PROCESSES
The article considers systems approaches to mathematical modelling of a real object (physical situation), applications of methods from the theory of geometrical modelling (ТGМ), nonlinear analysis of civil engineering objects geometrization problems, basic directions in the generalisation of geometric modelling, and issues in the parametrization of engineering models. The author also considers possibilities of generalisation of classical methods, including when going over from objects in three-dimensional space to varieties of arbitrary structure and dimensionality, replacement of the traditional method of projection with generalised methods of representation. Emphasis is made on mutual enrichment between the geometries of the original and the modelas a result of construction this or that reversible representation following from the formal equality if the object and the model. Specially noted are the possibilities of contemporary ITs, use of specialized automated facilities for processing spatial information and construction 3D digital models, and stages are identified in the organisation and realization of computations. The process of mathematical modelling is analysed. Consideration is given to the general flowchart of mathematical modelling and its main components are discussed. Examples from civil engineering practice are given to illustrate the characteristic stages in the process of mathematical modelling.
Key words: mathematical model, mathematical information modelling, systems analysis, geometric modelling, axiomatic method, constructive method, projection methods
1. Babich, V.N., Kremlev, A.G., Kholodova, L.P. (2011) Methodology of Systems Analysis in Architecture. [Online] Architecton: Proceedings of Higher Education, No. 34. Available at: http://archvuz.ru/2011_2/3
2. Babich, V.N., Kremlev, A.G. (2011) Systems Approach to Representation of University as an Educational System. In: Almanac of Contemporary Science and Education. Section: Pedagogy, Psychology, Sociology. Tambov: Gramota, No. 12 (55), p.87–91 (in Russian).
3. Babich, V.N., Kremlev, A.G. (2012) It-Based Mathematical Modelling for Addressing Architecture and Town-Planning Challenges [Online]. Architecton: Proceedings of Higher Education, No. 37. Available at: http://archvuz.ru/2012_1/5 (in Russian)