考虑流-结构耦合的体积约束拓扑优化

Volume-constrained topology optimization of fluid-structure coupled system

为实现流-结构耦合的结构拓扑优化设计,首先分别以水下结构固有频率和结构刚度最大化为目标,建立了渐进结构拓扑优化模型;然后,改进了网格独立滤波方法,提出单元尺寸滤波方法,将优化方法推广至设计域中单元尺寸存在差异较大情况的问题;最后,推导了目标函数以及在约束条件下的单元灵敏度,并采用双向渐进结构优化法对结构进行迭代计算。结果表明:刚度优化结果拓扑结构清晰,同时优化结构中未出现棋盘格现象,迭代过程收敛平稳;频率优化结果中,固有频率较初始设计域提升明显,优化效果显著,证明了单元尺寸独立滤波方法的有效性。

In order to realize the topology optimization of flow-structure coupling,firstly the progressive structure topology optimization model is set up with the aim of maximizing the natural frequency and structural stiffness of underwater structures.Then,the grid independent filtering method is improved,and the method of element size filtering proposed whereby the optimization method is exten-ded to the problem with large difference in the size of the elements in the design domain.Lastly,the objective function and the element sensitivity under the constraint conditions are derived,and the structure is iteratively calculated by the BESO method.The results show that the topology structure of the stiffness optimization results is clear,and the chessboard phenomenon does not appear in the optimization structure,and the iterative process is smooth and stable;in the results of frequency optimization,the natural frequency is improved obviously compared with the initial design domain and the optimization effect is remarkable.Numerical results demonstrate the effectiveness of the independent filtering method of cell size in this paper.