"Search for Solutions" in the Problems of Calculation of Building Structures

Abstract

Building structures are very diverse in their purpose and application. The reliability and safety of their operation depends on many factors: geometric dimensions, materials used, acting external loads and their combinations, etc. All these parameters determine the internal forces, stresses and strains that arise in structures, which determine their strength, rigidity and stability. In order to ensure the strength, rigidity and stability of buildings and their structural elements, appropriate calculations are performed. In the field of the theory of calculation of building structures, there is a constant refinement of the actual work of these structures, i.e. such design schemes are created that most accurately correspond to the actual operating conditions. The more optimally the design scheme is drawn up, the less time-consuming will be the stages of calculation and design of the corresponding structure. Therefore, the solution of the problem of optimization of design schemes is of great scientific and practical importance. One of the existing approaches to finding optimal solutions is discussed in the course "Operations Research". Operations Research deals with the development and application of methods for finding optimal solutions based on mathematical modeling. The operation model is an analytical dependence of the objective function on dependent (controlled) variables, which, within certain limits, we can choose at our discretion and set the range of their change. Solver is a Microsoft Excel add-in that can be used in Structural Analysis problems. With its help, you can find the optimal value (maximum or minimum) of the formula contained in one cell, called the target, taking into account restrictions on variable values in other cells. Simply put, with the Solver add-in, you can determine the maximum or minimum value of one cell by changing other cells. Most often, the add-on "Search for a solution" is used in solving optimization problems of the economy (simplex method, transport problem, etc. There are practically no results of using this approach in the calculations of building structures.