Discrete optimization problems of the steel bar structures

Abstract

In this paper there are considered the optimal design problems of the elastic and elastic-plastic bar structures. These problems are formulated as nonlinear discrete optimization problems. The cross-sections of the bars are designed from steel rolled profiles. The mathematical models of the problems, including the structural requirements of the strength, stiffness and stability, are formulated in the terms of finite element method. The stated nonlinear optimization problems are solved by the iterative method, where each iteration comprises of the selection of the cross-sections of the bars from the assortment and solution of linear problems of the discrete programming. The requirement of discrete cross-sections is ensured by the branch and bound method.