Physical and mathematical modeling is widely used in scientific research. This is due to the fact that field experiments on real construction sites are often impossible to organize for various reasons. The material included in the textbook is a summary of the authors ' experience in the field of system analysis. In the first section, the regularities of physical modeling of the functioning of objects based on the similarity and dimension theorems are considered. The second section presents modern models and methods for choosing optimal solutions: linear, nonlinear, stochastic, and statistical. The third section deals with experimental methods of system optimization based on the theory of experimental planning. Meets the requirements of the federal state educational standards of higher education of the latest generation. For students of higher educational institutions studying in the direction of training 08.04.01 "Construction", and graduate students of higher educational institutions. It will be useful for specialists in the field of mathematical methods for the study of complex systems and their applications.
The monograph deals with the development of models of stress-strain state of structural elements, the study of the behavior of building structures under the influence of dynamic loads using differential equations; methods of discretization of analytical models of the functioning of building structures and design of complex technical systems (system analysis problems). It is intended for scientific and technical workers, it will be useful to students in the areas of training 08.03.01 and 08.04.01 "Construction".
A new method for optimizing construction systems is proposed while taking into account the given level of reliability of their functioning. Proposed method is effective for problems in which the vector of optimal parameters of a building system belongs to one or more functional constraints. In practice, such tasks constitute a substantial majority. The main advantage of this method is that the construction costs for the production of the building system or its elements are minimal.
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