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实际的工程应用中,钢框架的基本构件大多是根据钢结构设计规范要求,从标准型钢库中选取,所组成的框架结构的截面尺寸非连续变化。因此,钢结构截面优化设计是典型的离散设计变量优化问题。若采用基于启发式的算法(如遗传算法等)进行求解,当可选截面类型较多时,其计算量巨大,求解效率低下。该文通过引入高维拉格朗日插值函数对该离散设计问题进行连续化,建立了可采用梯度优化方法进行求解的钢结构标准截面选型设计模型,并且使得连续化以后的设计变量个数大幅度减少。对给定截面类型种数为2n个的可选截面集合,其设计变量只需n个即可。具体算例表明:与基于遗传算法的优化方法相比,该方法的计算效率提高1~2个数量级,并且在结构性能基本相当的情况下,得到的型钢种类更少,便于工程应用。
In the actual engineering application, the basic components of the steel frame are mostly selected according to the requirements of the steel structure design specifications from the standard steel structure, and the sectional size of the frame structure formed by the non-continuous changes. Therefore, the optimal design of steel cross-section is a typical discrete design variable optimization problem. If the heuristic algorithm (such as genetic algorithm) is adopted to solve the problem, when there are many types of optional sections, the computational cost is huge and the solution efficiency is low. In this paper, by introducing the high-dimensional Lagrange interpolation function, the discrete design problem is continuous, a standard section design model of steel structure that can be solved by gradient optimization method is established, and the number of design variables decrease greatly. For a given set of 2n cross-section types, the design variables need only n. The concrete example shows that compared with the optimization method based on genetic algorithm, the computational efficiency of this method is improved by 1 ~ 2 orders of magnitude, and the types of steel obtained are less and the engineering application is more suitable when the structural performance is basically equal.