区间参数压电智能连续体多目标拓扑优化

摘要

研究具有区间参数的压电智能连续体结构/控制一体化多目标拓扑优化设计问题。构建以结构质量和二次型最优控制能量的上限极小化为目标函数,以结构的形状拓扑信息和控制器信息为设计变量,满足结构应力、控制器电压非概率可靠性为约束条件的区间参数受控结构的一体化多目标拓扑优化数学模型。基于泰勒展开和区间扩张,给出了应力、控制器电压的均值和离差,二次型最优控制能量区间的计算表达式。优化求解策略采用基于Pareto排序的多目标遗传算法。数值算例的结果表明了所提方法的可行性和有效性。%Multi-objective integrated optimization of piezoelectric smart continuum structures with interval parameters is studied.Based on non-probabilistic reliability,the integrated optimization mathematic model with stress and voltage constraints of piezoelectric smart continuum structures is constructed,where the upper bounds of the structure weight and the quadratic objective function are taken as objective functions and the structural element topology information,the number and placements of actuators and control gain are regarded as design variables.Through Taylor expansion and interval extension of function,the mean values and deviations of the stress for each element and the voltages for the piezoelectric active element,and the interval of the quadratic objective function can be obtained.The Pareto CMOPGA（genetic algorithm for constrained multi-objective optimization problem） on the basis of individual ranking is adopted to solve the constrained multi-objective optimization problem.The numerical example shows that the proposed method is effective and reasonable.