中文摘要：

以压电作动器为控制元件,建立了自适应桁架形状控制基本方程.考虑结构性状约束和电压限制,建立了以作动器位置和控制电压为设计变量,以形状精度、控制能量和作动器数目的加权表达式为目标函数的作动器优化配置数学模型.由于作动器和普通杆具有不同的单元刚度,作动器每一种不同的位置配置都会导致结构总刚度矩阵的变化,因此单独采用遗传算法需要进行大量的结构计算.为了减少结构分析次数,提出了多点近似、遗传算法和二次规划相结合的优化方法.算例结果表明本文方法具有很高的求解效率.

英文摘要：

With piezoelectric actuators as control elements, the basic equations of shape control for adaptive truss was formulated. A mathematical model of optimal actuator placements was presented, in which the actuator locations and the control voltages were taken as design variables, and the weighted presentation of the shape precision, control energy and number of actuators was taken as the objective function. This model subjected to the strength of the structure, the limit of nodal displacement and the maximum control voltage of actuators. Because the actuators and the ordinary bars have different element stiffness, every reasonable allocation of actuators could result in the change of whole stiffness matrix. If genetic algorithm was directly applied, an extremely large number of structural analysis would be needed. In order to decrease the number of structural analysis, a new method was proposed, in which the multi-point approximation, genetic algorithm and quadratic programming were combined. The results of examples show that the proposed method has high efficiency.