Applying conditional optimization to determine the allowable loads on flexurally rigid threads

Abstract

Objective. Development of a methodology for determining the allowable loads on existing structural elements, the design model of which is a flexural-rigid thread, based on the requirements of strength and rigidity due to the changed operating conditions of structures.Method. This study is based on mathematical modeling of the problem of conditional optimization. The objective function is the total potential energy of deformation of a thread with some flexural rigidity. In this case, restrictions are imposed on strength, rigidity, and the condition of continuity of deformations. At the same time, to achieve this goal, the provisions of the strength of materials, as well as the apparatus of integral and differential calculation of functions of one or more variables, were used.Result. An assessment of the adequacy of the results obtained using the developed methodology was carried out. A numerical experiment was performed to determine the value of the allowable uniformly distributed load and the corresponding distribution of stresses and strains along the length of a thread of finite stiffness with given physical and geometric parameters. It has been established that the discrepancies in the values of the results obtained using the proposed modeling technology and the commercial computer-aided design and calculation system LIRA 10.8, implemented on the generally recognized finite element method, are no more than 5%.Conclusion. The developed technique allows setting and solving problems of determining the ultimate loads on flexural-rigid threads, based on the allowable stresses and strains, in contrast to existing commercial computer simulation systems that solve exclusively direct problems of determining the stress-strain state of various types of structures. It can be used at the stage of inspection of large-span coatings in the reconstruction of public buildings and engineering structures.