流固耦合自重拓扑优化的区域包络线法  

Regional envelope method for self-weight topology optimization of fluid-structure coupling problems

作　　者：王旭东[1] 王德石[1] 刘宝 Wang Xudong;Wang Deshi;Liu Bao(School of Weaponry Engineering,Naval University of Engineering,430033,Wuhan,China;School of Electronic Engineering,Naval University of Engineering,430033,Wuhan,China)

机构地区：[1]海军工程大学兵器工程学院,武汉430033 [2]海军工程大学电子工程学院,武汉430033

出　　处：《应用力学学报》2020年第6期2591-2597,I0019,共8页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金青年基金资助项目(11602300)。

摘　　要：针对变边界流固耦合条件下双向渐进结构优化算法中流体域/结构域不能快速转换的问题,提出了一种区域包络线更新法,并将这种方法用于处理变边界流固耦合自重拓扑优化设计问题。建立了有限元耦合方程,采用拉格朗日乘子法将重力载荷的影响引入到目标函数中,分析了单元灵敏度公式。以结构体积为约束条件,水中结构柔顺度最小化为目标,着重对比了传统方法和提出的区域包络线更新法的计算效率,并研究了外界压力载荷、结构自重和水压力对优化结果的影响。研究结果表明:区域包络线法实现了拓扑优化过程中耦合边界的快速迭代更新,数值稳定性较好,相比于常规方法,计算代价大大降低;结构自重和水压力对优化结果都有重要影响,实际工程应用中两种载荷都要着重考虑。In order to solve the problem that the fluid-structure cannot be rapidly converted in the bidirectional asymptotic structure optimization algorithm with variable boundary fluid-structure coupling, a region envelope updating method is proposed to deal with the self-weight topology optimization design. The coupling equation is deduced and the effect of gravity load is introduced into the objective function by Lagrange multiplier method. The sensitivity formula of elements is derived. The goal is to minimize structural compliance in water. Effects of external pressure load, structural gravity and water gravity on the optimization results are compared emphatically. Results show that the region envelope method achieves fast iterative updating of the coupled boundary in the process of topology optimization, and the numerical stability is good. Compared with the traditional method, the calculation cost is greatly reduced. Structural gravity and water gravity have important effects on the optimization results, both loads should be considered in practical engineering applications.

关 键 词：区域包络 流固耦合 重力载荷 拓扑优化 变边界 

分 类 号：O242.21[理学—计算数学]