Некоторые особенности задачи оптимизации шпренгельных балок

Abstract

RU: Предложен алгоритм оптимизации шпренгельной балки, основанный на ее конструктивных особенностях и на требовании минимума изгибающих моментов. Узлы нижнего пояса располагаются на веревочной кривой. Параметрами оптимизации являются расстояния между стойками. Эффективность алгоритма подтверждается тестовым примером. Показано, что предложенный метод оптимизации обеспечивает также минимум объема шпренгельной балки.

EN: The authors proposed the algorithm of trussed beam optimization based on its design features and requirement of bending moment’s minimum. The statically determinate trussed beam was assumed in the article as a composite structure. The optimization was done under the constant loading. Nodes of truss bottom chord located on a funicular curve. Distances between pillars were assumed as optimization parameters. The materials cost for the truss beam construction, which consists of one material, is determined either by mass, or by volume. The optimization criterion of the truss beam with given topology will be the sum of the beam volumes and the truss, which are dependent on the variations of topology variables. The authors assumed that efficiency function (volume function) is smooth and continuous and its minimum is located in the point where all partial derivative from function of the unknown variables are equal to zero. The algorithm’s efficiency was confirmed by the test example. It is proved that the offered optimization method also helps to obtain minimum of trussed beam’s volume. Utilizing of described procedure helps to provide the logical design of structure optimization taking into account loading condition, combined loading and system indeterminacy.