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中文摘要：
对预应力平面实体钢结构拓扑优化设计问题进行研究，建立了以索力值、单元尺寸和结构拓扑为设计变量，以应力为约束条件，以结构重量最小为目标函数的教学优化模型。在求解方法上，首先以满应力设计准则法建立索力值与结构重量之间的优化模型，通过该模型的求解确定索力值，并通过满应力设计选取单元尺寸，然后对单元体厚度按阈值进行分类，从而删除低厚度单元实现结构的拓扑优化。算例结果与预应力钢结构理论相吻合，表明本文所提出的方法是有效的，可为预应力钢结构体系创新提供理论方法。
英文摘要：
A topology optimization design method for the prestressed plane entity steel structures is proposed. The optimization mathematical model is established in such form that the cables＇ pretension force, unit size and the structural topology are referred as the design variables, the element stress as constrain condition, the minimum of structural weight as the objective function. In order to solve the problem, firstly, an optimization model between calculate cables＇ pretension force and the structural weight is established by fully stress design, and cables＇ pretension force is calculated by solving the model and the unit size is selected by fully stress design, and then topology optimization design is completed through deleting lower thickness plane entity elements which classified according to threshold value. The result of the examples in this paper coincides with conclusion of corresponding structural performance, and this indicates the optimization design method in this paper is practicable and can provide theo- retical method for prestressed steel structures＇ system innovation.
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