Оптимізація будівельних конструкцій

Abstract

In the field of the theory of calculation of building structures, there is a constant refinement of the actual operation of these structures, i.e. design schemes are created that most accurately correspond to actual operating conditions. Creating optimal structures is a very urgent task facing designers. Therefore, it is quite natural to try to solve this problem using mathematical programming methods, which involve: selecting dependent and independent variables, constructing mathematical models and establishing criteria for the effectiveness of the selected model. In this case, the model should be a function that fairly accurately describes the research being carried out using mathematical apparatus (various types of functions, equations, systems of equations and inequalities, etc.). In mathematical programming, any set of independent (controlled) variables is called a solution. Optimal solutions are those that, for one reason or another, are preferable to others. The preference (effectiveness) of the study is quantified by the numerical value of the objective function. “Solution Search” is an add-in for Microsoft Excel that is used to solve optimization problems. Simply put, with the Solver add-in, you can determine the maximum or minimum value of one cell by changing other cells. Most often, this add-in is used to find optimal solutions to problems economically. There are not enough results of using this approach for calculating building structures in the public domain. Therefore, it is quite logical to try to use this add-on in problems of optimization of building structures. In this work, an attempt was made to use mathematical programming methods and this add-on to optimize the geometric dimensions of the structure, when the numerical value of the bending moment in a specific section was chosen as an optimization criterion.