离散变量桁架的形状优化设计

Shape optimization designs of trusses with discrete variables

提出了离散截面变量空间桁架形状优化的一个两级算法．在第一级优化中，固定节点的位置，以杆件面积为设计变量，进行离散变量截面优化；在第二级优化中，以节点坐标为设计变量，同时考虑截面变化；形成一系列优化子问题，按目标函数下降方向用Ｆｉｂｏｎａｃｃｉ法搜索出各坐标设计变量的最优变动值，从而形成新的节点位置．两级优化交替进行，直到收敛为止．算例表明本方法简单，收敛平稳，优化效果较好．在算例中讨论了不同的节点坐标初值对优化结果的影响及产生原因．

A two-level algorithm is proposed for shape optimization of space trusses with dis-crete sizing variables.At the first level,the cross-sectional areas are chosen to be the design vati-ables and the discrete sizing optimization is carried out under fixed joint positions.At the secondlevel,joint ccordinates are treated as design variables with changing cross-sectional areas to forma series of sub-problems in which the Fibonacci method is employed in the descent direction of theobjective to work out the optimal change of each coordinate variable and obtain new joint coordi-nates.The two levels are executed in turn until convergence is reached.The examples show thatthe proposed algorithm converges smoothly and gives satisfactory solutions.