Discretion Variable Optimization Design of Prestressed Steel Truss With Stress Constrains
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摘要: 对影响预应力钢桁架优化设计的2类变量,包括连续的索力值和离散的截面尺寸进行研究.建立了以应力和结构质量为约束条件、以最小化结构应变能为目标函数的数学优化模型.以杆件在预应力和外荷载共同作用下储存应变能最小确定施加在索上的预拉力.计算构件由于尺寸改变引起结构质量变化和应变能变化之比的相对差商,以此确定搜索方向.应用渐进结构优化法逐步调整构件截面尺寸,循环迭代,直至索力值和截面尺寸达到最优.算例与预应力钢结构理论结果相吻合,可为预应力钢结构工程设计提供最优的索力值和型钢的选择.Abstract: It is discussed the optimization design of prestressed cable supported steel truss with its design variables including continuous cables' pretension force and discrete cross section size.A optimization mathematical model is established in such a form that the member's stress and structural mass are constrain conditions and the minimum structural strain energy is the objective function.The cables' pretension force can be determined by minimizing all member bars strain energy when prestress and external load apply together.Each member's relative difference quotient which mass variations divide energy variations caused by the member's size change is calculated to determine searching direction.Evolutionary structural optimization is adopt to modify member cross section size gradually untill cables' pretension force and members' cross section size reach optimal by iteration.Result of examples in the paper coincides with that of prestress steel structures theory,the method in this paper can provide optimum cables' pretension force and formed steel for the prestressed steel structure design.
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