桁架材料和结构组合多目标优化设计

同时为桁架的每个杆件确定最为合适的材料和结构尺寸属于桁架材料和结构组合优化问题．提出一种桁架材料和结构组合多目标优化的方法．为材料分配唯一的标识编码，把杆件所用材料直接作为设计变量，并且和杆件截面积一起构成设计变量空间．考虑结构重量、成本和节点位移3个目标以及应力约束，建立了桁架材料和结构组合优化问题的数学模型．应用多目标遗传算法进行求解．算例结果表明，采用多目标遗传算法可以为桁架设计参数的确定提供多种选择方案，决策者可以根据目标的重要程度确定最后设计方案．算例分析结果验证了该方法的有效性．

Multi-Objective Optimal Design of Truss with Integrated Structure and Material Optimization

The integrated structure and material optimization of truss means determining and structural sizing variables simultaneously for each bar of truss. A method for integrated the optimal material structure and material optimization of truss was proposed. Each material type was assigned an ID number, and then both materials and cross-sectional areas were introduced as design variables. Three objectives including the structural weight, the cost and the deflection of nodes were considered under stress constraints. A mathematical model of the optimization problem was formulated. The problem was solved using a multi-objective genetic algorithm. The results show that the multi-objective genetic algorithm successfully generates various solutions for optimal design of truss. From these optimal solutions, decision makers can select the most suitable design according to the importance of the multiple objectives. The results of the numerical example demonstrate the feasibility of the proposed method.