流体流动中波状游动平板最优运动的数值方法  

Numerical Method for Optimum Motion of Undulatory Swimming Plate in Fluid Flow

作　　者：钱勤建[1] 孙德军[1] 

机构地区：[1]中国科学技术大学近代力学系,合肥230026

出　　处：《应用数学和力学》2011年第3期324-332,共9页Applied Mathematics and Mechanics

摘　　要：提出了一种求解波状游动平板最优运动方式的优化方法.最优化问题表述为固定推力的条件下,使得输入功率最小.由于存在不可见模态,使得该问题具有奇性,用通常的Lagrange乘子法计算得到的可能不是最优解,而是一个鞍点值.为了消除这一奇性,增加了一个关于幅值的不等式约束,并利用逐步二次规划的优化方法求解该问题.将该方法运用到二维和三维的波动板的几个例子上,获得了最优解.A numerical method for optimum motion of an undulatory swimming plate was presented.The optimal problem was stated as minimizing the power input under the condition of fixed thrust.The problem was singular for the invisible modes and the commonly used Lagrange method may not predict an optimum solution but just a saddle point.To eliminate the singularity,an additional amplitude inequality constraint was added to the problem.A numerical optimization code with a sequential quadratic programming method was used to solve the problem.The method was applied to several cases of two-dimensional and three-dimensional undulatory plates＇ motions and the optimum results were obtained.

关 键 词：波动板 最优化 面元法 逐步二次规划 

分 类 号：O352[理学—流体力学]