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对弹性和弹-塑性钢结构的优化设计问题进行探讨,将其归结为非线性离散优化问题。根据有限元方法,对问题的数学模型进行阐述,包括结构强度、刚度、稳定性。采用迭代法解决一些非线性优化问题,每次迭代时选择型钢的横截面,从分类到解决离散规划线性问题。通过分支定界法,确保得到所需的离散横截面。
The problem of optimal design of elasticity and elastic-plastic steel structure is discussed, which is attributed to nonlinear discrete optimization problem. According to the finite element method, the mathematical model of the problem is expounded, including the structural strength, stiffness and stability. Iterative methods are used to solve some nonlinear optimization problems. For each iteration, the cross section of the section steel is selected, and the linear problem of discrete programming is solved. By branch-and-bound method, it is ensured that the desired discrete cross-section is obtained.