【摘要】 本文提出线性化几何规划可行域修正系数法，对钢筋混凝土构件和框架进行了优 化设计。在其数学规划模型中，取总造价为目标函数，强度、配筋率、工艺构造等设 计规范要求为约束条件。这是一个高度非线性的规划问题，采用通常的数学规划法和 准则法都难以处理。 线性化几何规划的基本思想是利用缩并几何规划的理论和方法将具有正、负系数 多项式的目标函数和约束条件变换为单项函数．再将原设计变量进行对数变换，从而 转化为线性规划问题。但利用上述变换将多项式转化为单项式时，改变了原规划问题 的可行域。本法就是在每一步叠代过程中，利用可行域修正系数予以修正，使之与原 规划可行域趋近一致，因而避免了Ｄｅｍｂｏ收敛法在叠代运算中需不断增加新约束方 程而造成的困难，同时也避免了对偶几何规划“高困难度”的困难。更多还原

【Abstract】 In this paper the linearized geometric programming associated with correction coefficients of feasible region is adopted to solve the optimum design problems of reinforced concrete members and frames. The objective function is the total cost of the structure, including the costs of concrete, reinforcements and form work of construction. The constraints may be imposed from the strength, rigidity and technological requirements of the design code. This optimum design problem is a highly nonlinear programming and diffic- ult to deal with by usual method of mathematical programming or that of optimality criterion. In the aprroach of this paper, firstly the objective function and constra- ints with posynomials and signomials are condensed to single term function. Then the primal design variables are transformed into natural logarithm of the- mself’s. Accordingly the primal problem is reduced to a linear programming. But owing to the transformation of a posynomial into a single term, the feasible region of original program is modified, a revised Dembo’s method is proposed to make the necessary correction. In each step of the iteration, the linearized feasible region is modified by means of the correction coefficients of the fea- sible region. Instead of the primal nonlinear program a sequence of linear programs are obtained. The optimum design of a beam or a column with recta- ngular cross section can be accomplished by 5～9 iterations of linear progra- mming. Optimum desing of a frame with 5 stories and two spans and a frame with three stories and three spans have been made for illustration.更多还原